Flexible AC Transmission Systems FACTS 6

7/29/2019 Flexible AC Transmission Systems FACTS 6

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Distributed Power and FACTS

Opportunities offered by Flexible AC Transmission SystemsFACTS

FACTS refers to a range of controllers which control voltage, phaseangle, and series and shunt system impedance. Traditionally thiswas achieved with electromechanical equipment or thyristorcontrolled devices. Modern power electronic equipment offers theopportunity for extremely flexible power quality control. The IEEEdefinition for FACTS is:

Alternating current transmission systems incorporating power-

electronic based and other static controllers to enhance

controllability and increase power transfer capability.

The possible benefits from FACTS technology are as follows

Control of power flow Improved voltage control and stability Increase the loading capability of lines to their maximum

thermal capabilities Increasing transient stability margin Damping power oscillations Limiting short circuit currents Reduce reactive power flows Reduce current loop flow

These benefits are achieved with four basic type of controller: seriescontrollers, shunt controllers, combined series to series controllersand combined series-shunt controllers


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.

If we consider the general transmission system as depicted inFigure 1, then for negligible resistance (Z=jX) the phasor diagram is

as shown in Figure 2

Figure 2 The phasor diagram for transmission of power overa lossless transmission system

The power transfer equations are:2

sin( )A B

VP P

X (1)

E V

IAIB

SBSA

Source Load

A B

Z

Figure 1 Fundamental transmission system

Imaginary

EZI

IAn

/2 =An

/2

V

Real

= /2


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)cos(12

X

VQQ BA (2)

Note that in general is small. It, therefore, follows that the system

is controlled through the controllable parameters in the followingway.

Line impedance control through series reactors providescurrent control

Power angle control provides active power control Injecting a series voltage along the line with phase orthogonal

to the line current (reactive power injection) will control theline current and active power flow

Injecting a series voltage along the line with any phase withrespect to the line current (reactive and active powerinjection) will control the line current magnitude and phaseand active and reactive power flow

Injection of shunt reactive power can control the line voltageBecause the line impedance is normally relatively small the serie-connected controller MVA rating is normally quite small comparedwith the MVA control it can provide and the MVA rating necessaryfor a shunt connected controller. However, the series connecteddevice has the disadvantage that it must conduct full rated current.

Often a practical solution is a combination of series and shuntcontrollers.

Voltage Stability

FACTS controllers can improve voltage stability through the controlof shunt reactive power and system line impedance. For thefundamental system shown in Figure 1 the load voltage and andcurrent are given by

V E jXI (3)

*

P jQI

V

(4)

whereV*is the complex conjugate ofV. Assuming E is 1 p.u. thensolving equations (3) and (4) for V gives


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2

* 0V V jX P jQ (5)

The solution of equation (5) is multi-valued and typical results are

shown in Figures 3 and 4. Figure 3 shows the variation of linevoltage for the fundamental system with line impedance =j0.5 p.u.and for different load conditions. Similarly Figure 4 shows thevariation of line voltage for the fundamental system with lineimpedance =j0.4 p.u. and for different load conditions.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.2

0.4

0.6

0.8

1

1.2

Po wer (p.u.)

Voltage(p.u.)

Figure 3 Variation of line voltage for different load conditions(line impedance Z=j0.5 pu.

0.8 lag 0.9 leading

Unity pf


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0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

1.2

Po wer (p.u.)

Voltage(p.u.)

Figure 4 Variation of line voltage for different load conditions(line impedance Z=j0.4 pu.

The peak power output for a given power factor is the limit for thevoltage stability. The lower part of the curves (the other possiblevoltage level) represents an unstable condition. By comparingFigure 3 and Figure 4 it can be seen that voltage stability can beimproved by increasing the load power factor from lagging toleading or by reducing the line impedance.

Power Stability

Most electrical power is generated by rotating machines with a

rotational inertia. The system frequency is normally maintained bybalancing the electrical load powers Pe with the generator inputmechanical powers Pm. If there is a mismatch between the electrical

load and mechanical input powers then the rotating machines willaccelerate or decelerate with the energy added to or taken from therotational momentum of the machine. The equations of motion canbe derived as follows. For a machine of moment of inertia J (thisincludes the turbine as well as the rotor)and angular speed therate of change of rotation due to an applied total torque TT is given

by

0.8 lag0.9 leading

Unity pf


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Td

J Tdt

(6)

The total applied torque is due to the input mechanical torque (e.g.from the turbine) and the output mechanical torque from the

electrical load (a reaction torque on the rotor windings). This canbe better expressed in terms of input mechanical power PM andoutput electrical power PEby multiplying equation (6) by to give

( )T M E M E

dJ T T T P P

dt

(7)

From equation (7) it is clear that the rotating machines will be atconstant speed (d/dt=0) provided the input mechanical power

matches the output electrical power. For synchronous machines therotational speed of the rotor is directly related to the phase angle

of the stator emfEsuch that

0

d

dt

(8)

where 0 is the steady state frequency and alsoJ = M the angular

momentum of the machine. Thus we can write2

2 M E

dM P P

dt

(9)

The rotating machine will therefore accelerate when PM>PE and willdecelerate while PM


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P1. Because the system impedance changes the electrical outputpower changes to P2 after the switching operation. There is now

more input mechanical power than output electrical power so themachine will accelerate until the mechanical power equals theelectrical power at 2 after which it will decelerate until all the

excess kinetic energy is absorbed at 3. The gained kinetic energy isthen given by

2

1

2202

1( )2 2

m EM M P P d A

(12)

And the lost kinetic energy is given by

3

2

2 20 2

2( )2 2

m EM M P P d A

(13)

It follows therefore from equation 11 that the phase anglerepresents the point where the two areas A1 and A2 shown in the

figure are equal.

From equal area considerations it can be shown that FACTScontrollers improve the electrical power transfer such that the sizeof the oscillations is reduced.

Figure 5 Power swing due to switching operation as given bythe equal area criteria

A1

A2Stability margin

Load angle

Power

1

2

3

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Flexible AC Transmission Systems FACTS 6