Q10Power System Engineering

(a) Phase Shifting Transformer and its Applications

A phase shifting transformer (phase angle regulator) is a specialized transformer designed to introduce a controllable phase angle shift between its input and output voltage, without necessarily changing the voltage magnitude significantly, achieved by injecting a quadrature (90-degree-shifted) voltage component derived from one phase into the output of another phase, using a combination of an exciting unit (which taps voltage from the system, often with a tap-changer for adjustable magnitude) and a series unit (which injects this tapped, quadrature-related voltage in series with the main power path).

The fundamental principle exploited by a phase shifting transformer is that, in a transmission line connecting two buses, the real power flow along that line is primarily governed by the phase angle difference between the sending and receiving bus voltages (P approximately equal to V1V2sin(delta)/X, the same power-angle relationship examined in relation to transient stability elsewhere in this examination) - by deliberately introducing an additional, controllable phase angle shift at one end of a specific line (in addition to whatever phase angle difference already naturally exists across the line due to the surrounding network's normal power flow pattern), a phase shifting transformer can directly and deliberately control how much real power flows along that specific line, independent of the phase angles existing elsewhere in the network.

Applications of phase shifting transformers include: controlling (redirecting) real power flow among parallel transmission paths in a meshed network, specifically to prevent one lightly-loaded path from being underutilized while a parallel, more heavily-loaded path approaches its thermal limit (a common occurrence in meshed networks where power naturally divides among parallel paths according to their relative impedances, which may not match the desired or most efficient loading distribution); limiting loop-flow (unplanned, unwanted circulating power flow around a meshed network loop, often occurring in interconnected multi-utility systems where scheduled power transactions inadvertently cause flow along unintended paths due to the network's actual impedance-based flow-sharing behavior); and controlling power flow across international or inter-utility tie-lines to match scheduled interchange agreements precisely, particularly important where multiple parallel tie-lines exist between two interconnected control areas and the actual physical power flow distribution among them needs to be actively managed rather than simply left to follow the uncontrolled, impedance-determined natural flow pattern.

(b)(i) Shunt Capacitor

A shunt capacitor is a capacitor bank connected in parallel (shunt) across a bus or feeder, specifically to supply reactive power locally at that point in the network, compensating for the reactive power (lagging VARs) drawn by inductive loads (motors, transformers) and reducing the reactive power that would otherwise need to be transmitted from a remote generating source through the transmission and distribution network - since transmitting reactive power over a distance causes additional voltage drop and I-squared-R losses (exactly as transmitting real power does), supplying reactive power locally via shunt capacitors, close to where it is actually needed, directly improves voltage regulation at that point and reduces overall system losses. Shunt capacitors are widely used at distribution substations and along feeders (fixed or switched capacitor banks, the latter switched in and out automatically as load and voltage conditions vary through the day) as a low-cost, effective means of power factor correction and voltage support, though their reactive power output falls proportionally with the square of the actual system voltage (unlike a STATCOM or synchronous condenser, whose reactive output can be maintained more effectively even during a voltage sag), a limitation worth noting for their effectiveness precisely during the voltage-depressed conditions when reactive support may be most urgently needed.

(b)(ii) Series Capacitor

A series capacitor is a capacitor bank connected in series with a transmission line conductor itself (rather than in parallel/shunt across a bus), specifically to partially cancel out (compensate) the line's own inductive series reactance - since the line's total effective series reactance for power transfer purposes becomes (XL-Xc), where XL is the line's inductive reactance and Xc is the series capacitor's capacitive reactance, inserting a series capacitor directly reduces the effective transfer reactance of the line, which, from the power-angle relationship P=V1V2sin(delta)/Xeff examined elsewhere in this examination, directly increases the line's maximum power transfer capability (steady-state stability limit) for a given angle, and also improves voltage regulation along the line (since a lower effective series reactance means less voltage drop for a given transmitted current). Series capacitors are particularly valuable for increasing the power transfer capability of long transmission lines (whose naturally high series inductive reactance would otherwise significantly limit their maximum power transfer capability), though they require careful engineering attention to subsynchronous resonance risk (a potentially damaging torsional oscillation phenomenon that can occur between the series-compensated transmission network and nearby turbine-generator shaft systems, requiring specific mitigation measures such as subsynchronous damping controllers in certain series-compensated line applications near large thermal generating stations).

It is also worth noting that phase shifting transformers, shunt capacitors, and series capacitors together represent three distinct but complementary categories of passive and quasi-active power flow and voltage control equipment - phase shifting transformers primarily controlling real power flow distribution, shunt capacitors primarily providing local reactive power support and voltage boosting, and series capacitors primarily improving transfer capability and voltage regulation along a specific heavily loaded line - illustrating that a comprehensive power system voltage and power-flow control strategy typically deploys several of these complementary techniques together, in combination with the FACTS controllers (STATCOM, SVC, UPFC) examined in detail elsewhere in this course, rather than relying on any single technique alone to address the full range of voltage and power-flow control challenges present in a real transmission network.

Appreciating how these three distinct compensation and control technologies complement one another, rather than compete, is essential preparation for the more advanced FACTS-controller topics that build directly upon this foundational understanding.

This foundational understanding of passive and quasi-active compensation devices thus directly supports further study of modern power-electronic-based FACTS controllers.

Students who grasp this complementary relationship are well prepared to analyze more advanced, power-electronics-based compensation schemes later in the curriculum.

This closing perspective rounds out a complete picture of classical passive compensation techniques used throughout modern transmission networks.

Continued familiarity with these established compensation methods remains valuable even as newer power-electronic alternatives become increasingly widespread across modern transmission networks.