Quadrature booster

A quadrature booster, also known as a phase-shifting transformer or more simply a quad booster, is a specialised form of transformer used to control the flow of real power on three-phase electricity transmission networks.

For an alternating current transmission line, power flow through the line is proportional to the cosine of the difference in the phase angle of the voltage between the transmitting end and the receiving end of the line. Where parallel circuits with different capacity exist between two points in a transmission grid (for example, an overhead line and an underground cable), direct manipulation of the phase angle allows control of the division of power flow between the paths, preventing overload. [ B. M. Weedy, Electric Power Systems Second Edition, John Wiley and Sons, London, 1972, ISBN 0471924458 pages 127-128 ] Quadrature boosters thus provide a means of relieving overloads on heavily laden circuits and re-routing power via more favorable paths.

The capital cost of a quadrature booster can be high: as much as two or three million dollars for a unit rated over 2000 MVA. However, the utility to transmission system operators in flexibility and speed of operation, and particularly savings in permitting more economical dispatch of generation, can soon recover the cost of ownership.

Method of operation

By means of a voltage derived from the supply that is first phase-shifted by 90° (hence is in quadrature), and then re-applied to it, a phase angle is developed across the quadrature booster. It is this induced phase angle that affects the flow of power through specified circuits.

Arrangement

A quadrature booster typically consists of two separate transformers: a shunt unit and a series unit. The shunt unit has its winding terminals connected so to shift its output voltage by 90° with respect to the supply. Its output is then applied as input to the series unit, which, because its secondary winding is in series with the main circuit, adds the phase-shifted component. The overall output voltage is hence the vector sum of the supply voltage and the 90° quadrature component.

Tap connections on the shunt unit allow the magnitude of the quadrature component to be controlled, and thus the magnitude of the phase shift across the quadrature booster. The flow on the circuit containing the quadrature booster may be increased ("boost tapping") or reduced ("buck tapping"). Subject to system conditions, the flow may even be bucked enough to completely reverse from its neutral-tap direction.

Illustration of effect

The one-line diagram below shows the effect of tapping a quadrature booster on a notional 100 MW generator-load system with two parallel transmission lines, one of which features a quadrature booster (shaded grey) with a tap range of 1 to 19.

In the left-hand image, the quadrature booster is at its center tap position of 10 and has a phase angle of 0°. It thus does not affect the power flow through its circuit and both lines are equally loaded at 50 MW. The right-hand image shows the same network with the quadrature booster tapped down so to buck the power flow. The resulting negative phase angle has transferred 23 MW of loading onto the parallel circuit, while the total load supplied is unchanged at 100 MW. (Note that the values used here are hypothetical; the actual phase angle and transfer in load would depend upon the parameters of the quadrature booster and the transmission lines.)

References

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