FACTSFlexible AC Transmission

Systems

ByA.Immanuel

April 21, 2023 1

UNIT-IIISERIES COMPENSATION

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Shunt compensation is ineffective in controlling the actual transmitted power which, at defined transmission voltage, is ultimately determined by series line impedance and the angle between end voltage of the line.

Series compensation was Implemented in 1950It is Used to decrease transfer reactance of power line and there by increase the transmitted power.With FACTS initiative ,it has been demonstrated that variable series compensation is highly effective in

both controlling power flow in line and improving stability.

Series compensation

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OBJECTIVES OF SERIES COMPENSATIONAC power transmission over long lines was primarily limited by

the series reactive impedance of the line.Series capacitive compensation was introduced decades ago to

cancel a portion of the reactive line impedance and there by increase the transmittable power.

With FACTS initiative, it has been demonstrated that variable series compensation is highly effective in both controlling power flow in the line and in improving stability.

series line compensation can be applied to achieve full utilization of transmission assets by controlling the power flow in the lines, preventing loop flows and, with the use of fast controls, minimizing the effect of system disturbances, thereby reducing traditional stability margin requirements.April 21, 2023 4

In this chapter, The effect of series compensation on the basic factors, determining attainable maximal power transmission, steady-state power transmission limit, transient stability, voltage stability and power oscillation damping, will be examined.

Concept of Series Capacitive Compensation:The power transmission over a single line isThe effective transmission impedance Xeff with the series

capacitive compensation is given by

where k is the degree of series compensation, i.e.,

Assuming Vs = Vr = V , the current in the compensated line, and the corresponding real power transmitted, can be derived in the following forms:April 21, 2023 5

P = (V2/ X) sin δ

X eff =X - Xc Or Xeff = (1 - k)X

k = Xc/X O ≤ k ≤ 1

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Two-machine system with series capacitive compensation (a),corresponding phasor diagram (b), real power and series capacitor reactive power vs. angle characteristics (c).

P=Vm*I cos δ/2 =V.cos δ/2 *

The reactive power supplied by the series capacitor can be expressed as follows:

It can be observed that, as expected, the transmittable power rapidly increases with the degree of series compensation k.

Similarly, the reactive power supplied by the series capacitor also increases sharply with k and varies with angle δ in a similar manner as the line reactive power April 21, 2023 7

Voltage Stabilityshunt and series capacitive compensation can effectively increase

the voltage stability limit. Shunt compensation does it by supplying the reactive load

demand and regulating the terminal voltage. Series capacitive compensation does it by canceling a portion of

the line reactance and thereby, in effect, providing a "stiff” voltage source for the load.

For increasing the voltage stability limit of overhead transmiss- ion series compensation is much more effective than shunt comp- ensation of the same MVA rating.

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April 21, 2023 9Transmittable power and voltage stability limit of a radial transmissionline as function of series capacitive compensation

Improvement of Transient Stability

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Equal area criterion to illustrate the transient stability margin for a simple two-machine system, (a) without compensation, and (b) with a series capacitor

Power Oscillation Damping

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Waveforms illustrating power oscillation damping by controllable seriescompensation: (a) generator angle, (b) transmitted power, and (c) degree of series compensation.

VARIABLE IMPEDANCE TYPESERIES COMPENSATORS

GTO Thyristor-Controlled Series Capacitor (GCSC)An elementary GTO Thyristor-Controlled Series Capacitor, proposed

by Karady with others in 1992, is shown in Fig(a).The objective of the GCSC scheme is to control the ac voltage vc

across the capacitor at a given line current i.when the GTO valve, SW, is closed, the voltage across the capacitor .is

zero, and when the valve is open, it is maximum. The GTO valve is stipulated to close automatically (through

appropriate control action) whenever the capacitor voltage crosses zero.

However, the turn-off instant of the valve in each half-cycle is controlled by a (turn-off) delay angle l' (0 ≤ γ ≤ Π/2), with respect to the peak of the line current.

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Basic GTO-Controlled Series Capacitor (a), principle of turn-off delay angle control (b), and attainable compensating voltage waveform (c).

The TCR is a switch in series with a reactor, the GCSC is a switch in shunt with a capacitor.

The TCR is supplied from a voltage source (transmission bus voltage),the GCSC is supplied from a current source (transmission line current).

The TCR valve is stipulated to close at current zero, the GCSC at voltage zero.

The TCR is controlled by a turn-on delay with respect to the crest of the applied voltage, which defines the conduction interval of the valve.

The GCSC is controlled by a turn-off delay with respect to the peak of the line current, which defines the blocking interval of the valve.

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The TCR controls the current in a fixed inductor from a constant voltage source, thereby presenting a variable reactive admittance as the load to this source.

The GCSC controls the voltage developed by a constant current source across a fixed capacitor, thereby presenting a variable reactive impedance to this source.

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Thyristor-Switched Series Capacitor (TSSC)

The basic circuit arrangement of the thyristor-switched series capacitor is shown in Figure.

It consists of a number of capacitors, each shunted by an appropriately rated by pass valve composed of a string of reverse parallel connected thyristors, in series.

the degree of series compensation is controlled in a step-like manner by increasing or decreasing the number of series capacitors inserted.

A capacitor is inserted by turning off, and it is bypassed by turning on the corresponding thyristor valve.

A thyristor valve commutates "naturally," that is, it turns off when the current crosses zero. Thus a capacitor can be inserted into the line by the thyristor valve only at the zero crossings of the line current

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In order to minimize the initial surge current in the valve, and the corresponding circuit transient, the thyristor valve should be turned on for bypass only when the capacitor voltage is zero

The basic V-I characteristic of the TSSC with four series connected compensator modules operated to control the compensating voltage is shown in Figure (a1).

For this compensating mode the reactance of the capacitor banks is chosen so as to produce, on the average, the rated compensating voltage, VCmax = 4Xc Imin, in the face of decreasing line current over a defined interval Imin ≤I ≤ Imax

As the current Imin is increased toward Imax, the capacitor banks are progressively bypassed by the related thyristor valves to reduce the overall capacitive reactance in a step-like manner and thereby maintain the compensating voltage with increasing line current. April 21, 2023 18

The loss, as percent of the rated var output, versus line current characteristic of the TSSC operated in the voltage compensating mode is shown in Figure (a2) for zero voltage injection (all capacitors are bypassed) and for maintaining maximum rated voltage injection(capacitors are progressively bypassed).

The loss versus line current characteristic for this compensation mode is shown in Figure (b2) for zero compensating impedance (all capacitor banks are bypassed by the thyristor valves) and for maximum compensating impedance (all thyristor valves are off and all capacitors are inserted).

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The TSSC offers the following benefits compared to mechanically switched series capacitors:

The thyristor switches allow an unlimited number of operations without any wear. This capability is used to alter the degree of line compensation more frequently and to achieve a greater control over the power flow.

Exact switching instants (point-of-voltage waveforms) can be selected with thyristors, which significantly minimizes the switching transients. In contrast, the switching of mechanical breakers is unsynchronized.

A very rapid speed of response, in which the time between the initiation of a control signal and a capacitor insertion, or bypass, is typically less than a half-cycle (8 ms for 60 Hz).

No generation of harmonics.April 21, 2023 21

Thyristor-Controlled Series Capacitor (TCSC)

The basic Thyristor-Controlled Series Capacitor scheme, proposed in 1986 by Vithayathil with others as a method of "rapid adjustment of network impedance," is shown in Figure.

The basic idea behind the TCSC scheme is to provide a continuously variable capacitor by means of partially canceling the effective compensating capacitance by the TCR.

As we know, the TCR at the fundamental system frequency is a continuously variable reactive impedance, controllable by delay angle α.

The steady-state impedance of the TCSC is that of a parallel LC circuit, consisting of a fixed capacitive impedance, Xc, and a variable inductive impedance, XL(α), that is,April 21, 2023 22

effective reactive admittance, BL(α), for the TCR can be given by

XL = wL, and α is the delay angle measured from the crest of the capacitor voltage (or, equivalently, the zero crossing of the line current).

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Basic Thyristor-Controlled SeriesCapacitor scheme.

As the impedance of the controlled reactor, XL(α), is varied from its maximum (infinity) toward its minimum (wL).

the TCSC increases its minimum capacitive impedance, XTCSC.min = Xc = 1/wC, (and thereby the degree of series capacitive compensation) until parallel resonance at Xc = XL(α) is established and XTCSC.max theoretically becomes infinite.

Decreasing XL(α) further, the impedance of the TCSC, XTCSC(α) becomes inductive, reaching its minimum value of

XLXc/(XL - Xc) at α = 0, where the capacitor is in effect bypassed by the TCR.

Therefore, with the usual TCSC arrangement in which the impedance of the TCR reactor, XL, is smaller than that of the capacitor, Xc, the TCSC has two operating ranges around its internal circuit resonance: one is αClim ≤α≤π/2, where XTCSC(α) is capacitive, and the other is the

0 ≤α≤αLim range, where XTCSC(α) is inductive, as illustrated in Figure.April 21, 2023 24

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The impedance vs. delay angle ex characteristic of the TCSC

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SWITCHING CONVERTER TYPE

SERIES COMPENSATORSAs we know that a voltage-sourced converter with its internal

control can be considered a synchronous voltage source (SVS) analogous to an ideal electromagnetic generator.

It can produce a set of (three)alternating, substantially sinusoidal voltages at the desired fundamental frequency with controllable amplitude and phase angle; generate, or absorb, reactive power; and exchange real(active) power with the ac system when its dc terminals are connected to a suitable electric dc energy source or storage.

A functional representation of the SVS is shown in Figure.

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Functional representation of the synchronous voltage source based on a voltage-sourced converter.

References QRef and PRef (or other related parameters, such as the desired compensating reactive impedance Xref and resistance RRef) define the amplitude V and phase angle ψ of the generated output voltage necessary to exchange the desired reactive and active power at the ac output.

If the SVS is operated strictly for reactive power exchange, PRef (or RRef) is set to zero.

The function of the series capacitor is simply to produce an appropriate voltage at the fundamental ac system frequency in quadrature with the transmission line current in order to increase the voltage across the inductive line impedance, and thereby increase the line current and the transmitted power.

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The Static Synchronous Series Compensator (SSSC)

It was proposed by gyugyi in 1989.It uses the concept of converter-based technology uniformly for

shunt and series compensation, as well as for transmission angle control.

This device work the same way as the STATCOM. It has a voltage source converter serially connected to a transmission line through a transformer.

The basic operating principles of the SSSC can be explained with reference to the conventional series capacitive compensation of Figure above, shown simplified in Figure below together with the related voltage phasor diagram.

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Fig:Single line diagram of SSSCApril 21, 2023 31

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Fig 1:Basic two-machine system with a series capacitor compensated line and associated phasor diagram.

Fig 2:Basic two-machine system shown above but with synchronousvoltage source replacing the series capacitor.

The phasor diagram clearly shows that at a given line current the voltage across the series capacitor forces the opposite polarity voltage across the series line reactance to increase by the magnitude of the capacitor voltage.

Thus, the series capacitive compensation works by increasing the voltage across the impedance of the given physical line, which in turn increases the corresponding line current and the transmitted power.

it may be convenient to consider series capacitive compensation as a means of reducing the line impedance,in reality, as explained previously, it is really a means of increasing the voltage across the given impedance of the physical line.

It follows therefore that the same steady-state power transmission can be established if the series compensation is provided by a synchronous ac voltage source,as shown in Fig 2. whose outputApril 21, 2023 33

precisely matches the voltage of the series capacitor, i.e.,

Vq=Vc=-JXcI=-JkXI

Vc is the injected compensating voltage phasor,

I is the line current,

Xc is the reactance of the series capacitor,

X is the line reactance,

k = Xc/X is the degree of series compensation

In contrast to the real series capacitor, the SVS is able to maintain a constant compensating voltage in the presence of variable line current, or control the amplitude of the injected compensating voltage independent of the amplitude of the line current.

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For normal capacitive compensation, the output voltage lags the line current by 900.

For SVS, the output voltage can be reversed by simple control action to make it lead or lag the line current by 900.

In this case, the injected voltage decreases the voltage across the inductive line impedance and thus the series compensation has the same effect as if the reactive line impedance was increased.

With the above observations, a generalized expression for the injected voltage,Vq can simply be written

where Vq(ζ) is the magnitude of the injected compensating

voltage (0≤ Vq(ζ)≤Vqmax) and ζ is a chosen control parameter

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Vq = ±jVq (ζ)I/I

Transmitted Power Versus Transmission Angle CharacteristicThe SSSC injects the compensating voltage in

series with the line irrespective of the line current.The current in a line compensated at its

midpoint by the SSSC is expressed as

The corresponding line-power flow is then expressed as

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April 21, 2023 37Fig 3:

April 21, 2023 38At δ = 90°, k = 1/5 when Vq = 0.353 and k = 1/3 when Vq = 0.707.

Fig 4:

Comparison of the corresponding plots in Fig 3 and Fig 4 clearly shows that the series capacitor increases the transmitted power by a fixed percentage of that transmitted by the uncompensated line at a given Band.

The SSSC can increase it by a fixed fraction of the maximum power transmittable by the uncompensated line, independent of δ, in the important operating range of 0≤ δ ≤π/2.

The SSSC can decrease, as well as increase the power flow to the same degree, simply by reversing the polarity of the injected ac voltage.

The reversed (180° phase-shifted) voltage adds directly to the reactive voltage drop of the line as if the reactive line impedance was increased.

If this (reverse polarity) injected voltage is made larger than the voltage impressed across the uncompensated line by the sending-April 21, 2023 39

and receiving-end systems, that is, if Vq> lVs-Vrl, then the power flow will reverse with the line current I =(Vq-lVs-Vrl)/X, as indicated in Fig 4.

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SSSC could not be tuned with any finite line inductance to have a classical series resonance (at which the capacitive and inductive voltages would be equal) at the fundamental frequency, because the voltage across the line reactance would, in all practical cases, be greater than, and inherently limited by, the (fixed) compens-ating voltage produced by the SSSC. This compensating voltage is set by the control and it is independent of network impedance (and, consequently, line current) changes.

Control Range and VA Rating:The SSSC can provide capacitive or inductive compensating voltage independent of the line current up to its specified current rating.

Thus, in voltage compensation mode the SSSC can maintain the rated capacitive or inductive compensating voltage in the face of changing line current theoretically in the total operating range of zero to Iqmax, as illustrated in Fig(a1). •April 21, 2023 41

The practical minimum line current is that at which the SSSC can still absorb enough real power from the line to replenish its losses.

The corresponding loss, as percent of the (capacitive or inductive) rating of the SSSC, versus line current characteristic is shown in Fig(a2).

The VA rating of the SSSC (solid-state converter and coupling transformer) is simply the product of the maximum line current (at which compensation is still desired) and the maximum series compensating voltage: VA = ImaxVqmax

The SSSC is established to maintain the maximum rated capacitive or compensating reactance at any line current up to the rated maximum, as illustrated in Fig(b1). The corresponding loss versus line current characteristic is shown in Fig(b2).April 21, 2023 42

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Attainable V-I (compensating voltage vs. line current) characteristics of the SSSC when operated in voltage control (a 1) and reactance control (b1) modes, and the associated loss vs. line current characteristics (a2and b2, respectively).

It is seen in Fig above that an SSSC of 1.0 p.u. VA rating covers a control range corresponding to 2.0 p.u. compensating vars, that is, the control range is continuous from -1.0 p.u. (capacitive) vars to +1.0 p.u. (inductive) vars

series capacitors as part of the overall series compensation scheme, the SSSC may be combined cost effectively with a fixed capacitor, as illustrated in Figure

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Attainable V-I (compensating voltage vs. line current) characteristics of the hybrid series compensator of Figure above, when operated in voltage control (a1) and reactance control (bl ) modes, and the associated loss vs. line current characteristics (a2 and b2, respectively).

Capability to Provide Real Power Compensationseries capacitor functions in the transmission circuit as a reactive

impedance and as such is only able to exchange reactive power.the SSSC can negotiate both reactive and active power with the

ac system, simply by controlling the angular position of the injected voltage with respect to the line current.

However, the exchange of active power requires that the dc terminal of the SSSC converter be coupled to an energy source/ sink, or a suitable energy storage.

One important application is the simultaneous compensation of both active and resistive components of the series line impedance in order to keep the X/R ratio high.

In many applications, at transmission voltage levels of 115,230, and even 340 kV, where the X/R ratio is usually relatively low (in the range of 3 to 10). April 21, 2023 46

high degree of series capacitive compensation could further reduce the effective reactive to resistive line impedance ratio to such low values at which the progressively increasing reactive power demand of the line, and the associated line losses and possible voltage depression, would start to limit the transmittable active power. This situation is illustrated Fig below.

For a normal angle-controlled line whose uncompensated X/R ratio is 7.4. by applying series capacitive compensation (e.g., 50 and 75%), the effective Xeff /R =(XL - Xc)/R ratio decreases (to 3.7 and 1.85, respectively).

The reactive component of the line current, I sin(δ/2+φ), supplied by the receiving-end system, progressively increases and the real component, Icos (δ/2+φ), transmitted to the receiving end, progressively decreases with respect to those which would be obtained with an ideal reactive line (R = 0).April 21, 2023 47

April 21, 2023 48Transmitted real power P and reactive power Q vs. transmission angle B as a parametric function of the line XIR ratio.

The SSSC with an appropriate dc power supply would be able to inject, in addition to the reactive compensating voltage, a component of voltage in anti phase with that developed across the line resistance to counteract the effect of the resistive voltage drop on the power transmission

The power loss I2R would, of course, still be dissipated by the physical line. However dissipated power would be replenished by the SSSC from the auxiliary power supply.

The real power compensation capability could also be used effectively in minimizing loop power flows by balancing both the real and reactive power flows of parallel lines.

Reactive line compensation combined with simultaneous active power exchange can also enhance power oscillation damping.

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Oscillograms from TNA simulation showing the capability of the SSSCto provide both reactive and resistive series line compensation.

The TNA simulation of a two machine system compensated by the SSSC with a dc power supply, illustrated above the combined compensation of the line reactance and resistance.

During the periods of angular acceleration, the SSSC with a suitable energy storage can apply maximum capacitive line compensation to increase the transmitted active power and concurrently absorb active power to provide the effect of a damping resistor in series with the line.

During the periods of angular deceleration, the SSSC can execute opposite compensating actions, that is, apply maximum inductive compensation to decrease the transmitted active power and concurrently provide the effect of a negative resistance (i.e., a generator) to supply additional active power for the line (negative damping).April 21, 2023 51

Immunity to Sub synchronous Resonance

The function of the series capacitor is to provide a compensating voltage opposite to that which develops across the reactive line impedance at the fundamental system frequency to increase the transmitted power

the impedance of the series capacitor is a function of frequency and thus it can cause resonances at various sub synchronous frequencies with other reactive impedances present in the network.

the inherent frequency characteristic of the series capacitor in the dominant sub synchronous frequency band by a parallel connected thyristor-controlled reactor, making it immune to sub synchronous resonance with the use of electronic control.April 21, 2023 52

The voltage-sourced converter-based static synchronous series compensator is essentially an ac voltage source which, with a constant dc voltage and fixed control inputs, would operate only at the selected (fundamental) output frequency, and its output impedance at other frequencies would theoretically be zero.

The SSSC does have a relatively small inductive output impedance provided by the leakage inductance of the series insertion transformer.

The voltage drop across this impedance is automatically compensated at the fundamental frequency when the SSSC provides capacitive line compensation.

SSSC is unable to form a classical series resonant circuit with the inductive line impedance to initiate subsynchronous system oscillations.April 21, 2023 53

Internal ControlThe discussion on subsynchronous resonance indicates that the

implementation of some SSR immunity strategies requires the full (magnitude and angle) controllability of the compensating voltage the SSSC generates.

For output voltage control, converters may be categorized as "directly" and "indirectly" controlled.

For directly controlled converters both the angular position and the magnitude of the output voltage are controllable by appropriate valve (on and off) gating.

For indirectly controlled converters only the angular position of the output voltage is controllable by valve gating; the magnitude remains proportional to the dc terminal voltage.

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The control method of maintaining a quadrature relationship between the instantaneous converter voltage and line current vectors, to provide reactive series compensation and handle SSR, can be implemented with an indirectly controlled converter.

The method of maintaining a single-frequency synchronous (i.e., fundamental) output independent of dc terminal voltage variation, requires a directly controlled converter.

high-power directly controlled converters are more difficult and costly to implement than indirectly controlled converters (because their greater control flexibility is usually associated with some penalty in terms of increased losses, greater circuit complexity, and/or increased harmonic content in the output).

A possible internal control scheme for the indirectly controlled SSSC converter is shown in Fig below.April 21, 2023 55

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Functional internal control scheme for the SSSC employing an indirectly controlled converter

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Functional internal control scheme for the SSSC employing a directly controlled converter

EXTERNAL (SYSTEM) CONTROL FOR SERIES

REACTIVE COMPENSATORSthe external control that defines the functional operation of the

compensator and derives the reference input for it can basically be the same for all types of series compensator.

Additional functions for the improvement of transient (first swing) and dynamic stability (power oscillation damping) and, in some cases, for the damping of subsynchronous oscillation may be included in the external control of the series compensator.

A possible structure of the external control is illustrated in Figure below.

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Functional external (system) control scheme for the SSSC.

UPFC has following features.

Instantaneous speed of response

Extended functionality

Capability to control voltage, line impedance and

phase angle in the power system network

Enhanced power transfer capability

Ability to decrease generation cost

Ability to improve security and stability

Applicability for power flow control, loop flow

control, load sharing among parallel corridors

UPFC

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UPFC STRUCTUREThe general structure of UPFC contains back to

back AC to DC voltage source converters

operated from a common DC link capacitor.

The general structure of UPFC is shown in Fig.

Fig : Circuit Diagram of Unified Power Flow Controller (UPFC)April 21, 2023 61

Fig Implementation of the UPFC by two back-to-back voltage-sourced converters

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In the presently used practical implementation, the UPFC consists of two voltage-sourced converters using gate turn-off (GTO) Thyristor valves.

These converters, labeled “converter1” and “converter2”, are operated from a common dc link provided by a dc storage capacitor.

This arrangement functions as an ideal ac to ac power converter in which the real power can freely flow in either direction between the ac terminals of the two converters, and each converter can independently generate (or absorb) reactive power at its own ac output terminal

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Converter2 provides the main function of the UPFC by injecting a voltage

Vpq with controllable magnitude and phase angle P in series with the line

via an insertion transformer.

This injected voltage acts essentially as a synchronous ac voltage source.

The transmission line current flows through this voltage source resulting in

reactive and real power exchange between it and the ac system.

The reactive power exchanged at the ac terminal (i.e., at the terminal of the

series insertion transformer) is generated internally by the converter.

The real power exchanged at the terminal is converted into dc power which

appears at the dc link as a positive or negative real power demand.

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The basic function of converter 1 is to supply or absorb the real power demanded by converter 2 at the common dc link.

This dc link power is converted back to ac and coupled to the transmission line via a shunt-connected transformer.

Converter 1 can also generate or absorb controllable reactive power, if it is desired, and thereby provide independent shunt reactive compensation for the line.

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Different operating modes of UPFC Active and reactive power flow control Power flow control by voltage shifting General Direct Voltage Injection Direct Voltage Injection with Vse in phase with Vi

Direct Voltage Injection with Vse in Quadrature with Vi

Voltage Regulation with Vse in phase with Vi

Phase Shifting Regulation Line Impedance Compensation

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There fore the series converter has following control modes

Direct Voltage control mode .Line impedance emulation mode.Phase angle Shift emulation mode.Power flow control mode

Shunt converter has following control modesReactive power control mode.Voltage control mode.

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Fig : Equivalent circuit of UPFC April 21, 2023 68

Various Applications of UPFC

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