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Home / Technical Articles / Where and Why Do We Use Phase-Shifting Transformers?

Basic Principle of Application

Because of the predominantly inductive character of the power system, an active power flow between source and load must be accomplished with a phase lag between the terminals. Phase-shifting transformers are a preferred tool to achieve this goal.

Where and Why Do We Use Phase-Shifting Transformers
Where and Why Do We Use Phase-Shifting Transformers (photo credit: BTW Atlanta)

Two principal configurations are of special interest:

  1. The power flow between transmission systems operating in parallel where one system includes a PST and
  2. Where a single transmission line which includes a PST is connecting two otherwise independent power systems.

The latter is in fact a special case of the first, but it has become more important nowadays for the interconnection of large systems. For the following considerations, it is assumed that the ohmic resistance R is small compared with the reactance X and thus has been neglected.

Situation – One practical basic situation is that a location where power is needed (load side) is connected to the source side through two systems that need not necessarily have the same rated voltage level.

See Figure 1 below.

Parallel systems
Figure 1 – Parallel systems

Without any additional measure, the currents I1 and I2 would be distributed in proportion to the ratio of the impedances of the systems,

I1 = I × X2/(X1 + X2)
I2 = I × X1/(X1 + X2)

and there is no doubt that system 2 would take only a small part of the load because of the additional impedances of the two transformers in that branch.

If the power flow in system 2 should be increased, an additional voltage ΔV must be introduced to compensate the increased voltage drop in system 2.

Presuming that active power should be supplied to the load side and considering the inductive character of the systems, this voltage must have a 90° phase lag to the line-to-ground voltages of the system (VL).

In principle, the source of ΔV could be installed in each of the two systems. Figure 2 shows the voltage diagrams of both options. Figure 2a corresponds to Figure 1 with the PST installed in system 2, the system with the higher impedance. The additional voltage reduces the voltage drop in system 2 to that of system 1.

The voltage at the output or load side of the PST VL* leads the voltage at the input or source side VS. Per definition, this is called an advanced phase angle. If the PST were installed in system 1 (Figure 2b), the additional voltage would increase the voltage drop to that of system 2.

In this case, the load-side voltage VL* lags the source side voltage VS, and this is defined as retard phase angle. As can also be seen from the diagrams, an advanced phase angle minimizes the total angle between source and load side.

No-load voltage diagram of parallel systems
Figure 2 – No-load voltage diagram of parallel systems

The second important application is the use of a PST to control the power flow between two large independent grids (Figure 3). An advanced phase angle is necessary to achieve a flow of active power from system 1 to system 2.

Connection of two systems
Figure 3 – Connection of two systems

Types of Phase-Shifting Transformers

General Aspects

The general principle to obtain a phase shift is based on the connection of a segment of one phase with another phase. To obtain a 90º additional voltage ΔV, the use of delta-connected winding offers the simplest solution.

Figure 4 shows a possible arrangement and is used to introduce a few basic definitions. The secondary winding of phase V2 – V3 is split up into two halves and is connected in series with phase V1. By designing this winding as a regulating winding and using on-load tap changers (OLTC), ΔV and the phase-shift angle can be changed under load.

The phasor diagram has been plotted for no-load conditions, i.e., without considering the voltage drop in the unit. It also should be noted that the currents in the two halves of the series winding are not in phase.

This is different from normal power transformers and has consequences with respect to the internal stray field.

Single core symmetrical PST - Phase-Shifting Transformer
Figure 4 – Single core symmetrical PST – Phase-Shifting Transformer

VS1 = V10 + (ΔV1/2)

VL1 = V10 − (ΔV1/2)

ΔV1 = VS1 −VL1

From the phasor diagram (Figure 4b) follows (VS1 = VL1 = V):

V0 = V × cos(α/2)

ΔV = V × 2 × sin(α/2)

VΔ = V × cos(α/2) × √3

and with IS = IL = I, the part of the current that is transferred to the exciting winding becomes:

IΔ = (ΔV/VΔ) × I × cos(α/2) = I × (2/√3) × sin(α/2)

The throughput power can be calculated from

PSYS = 3 × V × I

and the rated design power, which determines the size of the PST, becomes

PT = 3 × ΔV × I = PSYS × 2 × sin(α/2)

A third kind of power (PΔ) is the power that is transferred into the secondary circuit. This power is different from PT because a part of the primary current is compensated between the two parts of the series winding itself.

In two-core designs (Equation ΔV1 = VS1 −VL1), this power determines also the necessary breaking capability of the OLTC.

PΔ = VΔ × IΔ = 1/3 × PSYS × sin(α)

In addition to the transferred power, the phase-shift angle is also important.

A phase-shift angle of 20° means that the PST has to be designed for 34.8% of the throughput power, and an angle of 40° would require 68.4%. In this respect, it has to be considered that the effective phase-shift angle under load is smaller than the no-load phase-shift angle.

In the optimum case when the load power factor is close to 1, a PST impedance of 15% would reduce the load phase-shift angle by 8.58.

In practice, various solutions are possible to design a PST. The major factors influencing the choice are:

  1. Throughput power and phase-shift angle requirement
  2. Rated voltage
  3. Short-circuit capability of the connected systems
  4. Shipping limitations
  5. Load tap-changer performance specification

In addition, preferences of a manufacturer as to the type of transformer (core or shell) or type of windings and other design characteristics may also play a role.

Depending on the rating, single- or two-core designs are used. Two-core designs may require either a one-tank or a two-tank design.

Single-Core Design

Symmetrical conditions are obtained with the design outlined in Figure 4a. Figure 5a and Figure 5b show the general connection diagrams with more details of the regulating circuit.

The advantage of the single-core design is simplicity and economy. But there are also a number of disadvantages.

Disadvantages – The OLTCs are connected to the system and directly exposed to all overvoltages and through faults. The voltage per OLTC step and the current are determined by the specification and do not always permit an optimal economical choice of the OLTC. The short-circuit impedance of the PST varies between a maximum and zero.

Therefore, it can not be planned that the PST will contribute to the limitation of fault currents in the system.

The advantage of the symmetrical design (Figure 5a) is that the phase-shift angle is the only parameter that influences the power flow. The design needs two single-phase OLTCs (for low ratings, one two-phase OLTC may be used instead) per phase or two three-phase OLTCs.

(a) Single-core symmetrical PST (b) Single-core unsymmetrical PST
Figure 5 – (a) Single-core symmetrical PST (b) Single-core unsymmetrical PST

Figure 5b shows an unsymmetrical solution. Only one-half of the regulating windings is used. The number of necessary OLTCs is reduced, but the ratio between source voltage and load voltage changes with the phase-shift angle and additionally influences the power flow.

A solution that often is used for transformers interconnecting two systems is shown in Figure 6.

The tap winding of a regulating transformer can be connected to a different phase, causing a voltage shift between the regulated winding and the other windings of the unit.

Regulating transformer with PST effect
Figure 6 – Regulating transformer with PST effect

The regulated winding normally is connected to the source side, but indirect regulation of the load-side is also possible. The change from the normal regulating transformer state to the phase-shifting state is possible in the middle position of the OLTC without the need to switch off the unit.

Another solution of a symmetrical PST, the delta-hexagonal phase-shifting transformer, is shown in Figure 7.

Delta-hexagonal PST
Figure 7 – Delta-hexagonal PST

Two-Core Design

The most commonly used circuit for a two-core design is shown in Figure 8 below. This configuration consists of a series unit and a main unit. For smaller ratings and lower voltages, two-core PSTs can be built into a single tank, while larger ratings and higher-voltage PSTs require a two-tank design.

The advantage of a two-core design is the flexibility in selecting the step voltage and the current of the regulating winding. These can be optimized in line with the voltage and current ratings of the OLTC.

Since OLTCs have limited current ratings and step voltages per phase as well as limited switching capacity, they are the main limiting features for the maximum possible rating of PSTs. More than one OLTC per phase may have to be utilized for very large ratings.

Two-core PST
Figure 8 – Two-core PST

Up to a certain rating, three-pole OLTCs can be used. For higher ratings, three single-pole OLTCs are necessary. The OLTC insulation level is independent of the system voltage and can be kept low. The short-circuit impedance is the sum of the impedances of the main and series transformers.

Because the impedance of the series unit is constant and independent from the phase angle, the unit can be designed to be self-protecting, and the variation of the impedance with the phase-shift angle can be kept small when the impedance of the main unit is kept low.

Quadrature Booster Transformers

Quadrature booster transformers are a combination of a regulating power- or auto-transformer with a phase-shifting transformer. The PST, which can be a single- or two-core design, is supplied from the regulated side of the power transformer (Figure 9).

Quadrature booster—simplified connection diagram
Figure 10 – Quadrature booster—simplified connection diagram

By this method, the output voltage can be adjusted in a four-quadrant (magnitude and phase) relationship.

Reference // Electric Power Engineering Handbook by Leonard L. Grigsby (Purchase hardcopy from Amazon)

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Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.


  1. Digambar P. Wavhal
    Jul 09, 2020

    very useful article

    Jul 09, 2020

    Lofty thanks for the in depth knowledge

    May 31, 2020

    Quite Usefull article. Thankyou

  4. Islavath Jayaprakash
    Jul 06, 2019

    Thank u sir for providing us with useful nd verygood explaination

  5. M Manena
    Jul 06, 2019

    I’m really finding the information provided here so useful, the technical analysis is on point, thank you sir

  6. Digambar P Wavhal
    Jul 06, 2019

    very useful article

    • D. P. WAVHAL
      Jul 09, 2020

      I have read your article of phase shifting transformer I am very much impressed with this article .
      This is the addition in the technical knowledge Bank.

  7. Er.Nagnath K
    Jul 06, 2019

    Thnx sir,
    For giving detail knowledge about phaseshifting transformer. Keep it up…. !!!

  8. Engr. Akwu J. A
    May 29, 2018

    I have found the site so rich and interesting, and I also like the technical details analysis of Power systems. keep it up sir

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