STUDY OF POWER SYSTEM STABILITY USING SVC

Mohd Afzal Biyabani (g200904750)

King Fahd University of Petroleum and Minerals.

Keywords: Power system stability, FACTS, SVC, Stabilizer.

ABSTRACT:

The paper presents a fundamental analysis of the application of static VAR compensators (SVC) for stabilizing power systems. Basic SVC control strategies are examined in terms of enhancing the dynamic and transient stabilities. SVC is basically a shunt connected static var generator whose output is adjusted to exchange capacitive or inductive current so as to maintain or control specific power variable; typically, the control variable is the SVC bus voltage. One of the major reason for installing a SVC is to improve dynamic voltage control and thus increase system load ability There are the mainly accomplishes work to construct an effective for SVC. Firstly, to design a controller for SVC devices on transmission lines,a Single Machine Infinite Bus (SMIB) system is modeled. A state space mathematical model is constructed and a Program in MATLAB is written to show the improvement in the dynamic performance of the system.

INTRODUCTION:

Advances in power electronics have introduced powerful tools to the electric energy transmission and distribution industry. One of the major products recently applied is the Thyristor-Controlled Reactive Power Compensators or Static VAR Compensators (SVC). A Static VAR

Compensator (or SVC) is an electrical device for providing fast-acting reactive power on high voltage electricity transmission networks. SVC are the part of Flexible AC Transmission Systems, regulating voltage and stabilizing the system. It is an impedance matching device, designed to bring the system closer to unity power factor. If the power system's reactive load is capacitive (leading), the SVC will use reactors to consume VAR’s from the system, lowering the system voltage. Under inductive (lagging) conditions, the capacitor banks are automatically switched in, thus providing a higher system voltage. They also may be placed near high and rapidly varying loads, such as arc furnaces where they can smooth flicker voltage.

SVCs are used for:

1. Increasing power transfer in long lines.

2. Stability improvement(both steady state and transient) with fast acting voltage regulation.

3. Damping of low frequency oscillations (corresponding to elctromechanical modes).

4. Damping of subsynchronous frequency oscillations (due to torsional modes).

5. Control of dynamic overvoltages.

The Single Machine Infinite Bus (SMIB) Power system model is considered and a SVC is installed at the centre of the transmission lines. The model is mathematically developed and the controller is designed.

Flexible AC transmission system (FACTS):

A flexible alternating current transmission system (FACTS) is a system composed of static equipment used for the AC transmission of electrical energy. It is meant to enhance controllability and increase power transfer capability of the network. It is generally a power electronics- based system.

FACTS is defined by the IEEE as "a power electronic based system and other static equipment that provide control of one or more AC transmission system parameters to enhance controllability and increase power transfer capability.

Series compensation:

In series compensation, the FACTS is

connected in series with the power system. It

works as a controllable voltage source.

Series inductance occurs in long

transmission lines, and when a large current

flow causes a large voltage drop. To

compensate, series capacitors are connected.

Examples:

Thyristor-controlled series capacitor

(TCSC)

Thyristor-controlled series reactor

(TCSR)

Thyristor-switched series capacitor

(TSSC):

Shunt compensation:

In shunt compensation, power system is

connected in shunt (parallel) with the

FACTS. It works as a controllable current

source. Shunt compensation is of two types:

Shunt capacitive compensation:

This method is used to improve the power

factor. Whenever an inductive load is

connected to the transmission line, power

factor lags because of lagging load current.

To compensate, a shunt capacitor is

connected which draws current leading the

source voltage. The net result is

improvement in power factor.

Shunt inductive compensation:

This method is used either when charging

the transmission line, or, when there is very

low load at the receiving end. Due to very

low, or no load – very low current flows

through the transmission line. Shunt

capacitance in the transmission line causes

voltage amplification (Ferranti Effect). The

receiving end voltage may become double

the sending end voltage (generally in case of

very long transmission lines). To

compensate, shunt inductors are connected

across the transmission line.

Examples:

Static synchronous compensator

(STATCOM).

Static VAR compensator (SVC).

Static VAR Compensator:

Basic Configuration:

Typically, a SVC comprises a bank of individually switched capacitors in conjunction with a thyristor -controlled air- or iron-core reactor. By means of phase angle modulation switched by the thyristors, the reactor may be variably switched into the circuit, and so provide a continuously variable MVAR injection (or absorption) to the electrical network. In this configuration, coarse voltage control is provided by the capacitors; the thyristor-controlled reactor is to provide smooth control. Smoother control and more flexibility can be provided with thyristor-controlled capacitor switching.

Fig 1. One line diagram of a typical SVC configuration; here employing a thyristor-controlled reactor with a bank of three mechanically-switched capacitors.

The combination of thyristor-controlled capacitors and reactors makes it possible to set any desired operating point over a predetermined VAr range within its capacitive and inductive limits. The only constraint is that the TCR rating can fully compensate the capacitive rating or that a switchable capacitor bank is graded accordingly.

SVC V-I Characteristic

The SVC can be operated in two different modes: In voltageregulation mode and in var control mode (the SVC susceptance is kept constant) When the SVC is operated in voltage regulation mode, it implements the following V-I characteristic. As long as the SVC susceptance B stays within the maximum and minimum susceptance values imposed by the total reactive power of

capacitor banks (Bcmax) and reactor banks (Blmax), the voltage is regulated at the reference voltage Vref. However, a voltage droop is normally used (usually between 1% and 4% at maximum reactive power output), and the V-I characteristic has the slope indicated in the Figure.5. The V-I characteristic is described by the following three equations:

SVC is in regulation range (-Bmax< B <BLmax)

V I /BcmaxV=Vref +Xs . I

SVC is fully capacitive (B=Bcmax)

V=I / Blmax

SVC is fully inductive (B=BLmax)Where,V = Positive sequence voltage (p.u.)I = Reactive current (p.u./Pbase) (I > 0 indicates an inductive current)Xs = Slope or droop reactance (p.u./Pbase)BCmax = Maximum capacitive susceptance (p.u./Pbase) with all TSCs in service, no TSR or TCRBLmax = Maximum inductive susceptance (p.u./Pbase) with all TSRs in service or TCRs at full conduction, no TSCPbase = Three-phase base power

Fig 2. V-I characteristics of SVC

Advantages of SVC:

The main advantage of SVCs over simple

mechanically-switched compensation

schemes is their near-instantaneous response

to changes in the system voltage. For this

reason they are often operated at close to

their zero-point in order to maximize the

reactive power correction they can rapidly

provide when required.

They are in general cheaper, higher-

capacity, faster, and more reliable than

dynamic compensation schemes such

as synchronous condensers.

POWER SYSTEM MODEL:

Power Improvement Using SVC:

An SVC can be used to enhance the powr

transfer capacity of a transmission line,

which is also characterized as the steady

state power limit. Consider a single machine

infinite bus (SMIB) system with an

interconnecting lossless tie line having

reactance X shown in the figure.

Fig 3. Single machine infinite bus system (a) an

uncompensated system and (b) an SVC compensated

system.

Let the voltages of the synchronous

generator and infinite bus be V1 at an angle δ and V2 respectively. The power

transferred from the synchronous machine to

the infinite bus is expresses as

P=(V 1∗V 2X )∗sinδ

If v1=v2=v then,

P=( V 2/ X )∗sinδ

At δ=90 degrees

Pmax= (V 2/ X )

Now let the transmission line be

compensated at its midpoint by an ideal

SVC. The term ideal corresponds to an SVC

with an unlimited reactive power rating that

can maintain the magnitude of the midpoint

voltage constant for all real power flow

across the transmission line. The SVC bus

voltage is then given by Vm at an angle δ/2.

The power flow across the half line section

connecting the generator and the SVC is

expressed as

Pc=(V 1∗V 2X /2 )∗sinδ /2

The power transfer in the other half line

section interconnecting the SVC and the

infinite bus is also described by a similar

equation. Assuming further that

Vm=V1=V2=V, then

Pc=( v2∗1X /2 )∗sinδ /2

Which is depicted graphically as shown

below . The maximum transmittable power

across the line is then given by

Pcmax=( V 2

X /2 )∗sinδ /2

Which is twice the maximum power

transmitted in the uncompensated case and

occurs at δ2=90degrees. In other words the

midpoint located ideal SVC doubles the

steady state power limit and increases the

stable angular difference between the

synchronous machine and the infinite bus

from 90 to 180 degrees.

If the transmission line is divided into ‘n’

equal sections, with an ideal SVC at each

junction of these sections maintaning a

constant voltage magnitude V then the

power transfer Pc’ of this line can be

expresses as

Fig 4. The variation of line real power flow and

SVC reactive power flow in a SMIB system

P c '= v2

( xn )sin ( δ

2 )

It can be shown that the reactive power requirement Qsvc of the midpoint SVC for the voltage stabilization is given by

Qsvc=4 v2

x∗(1−cos( δ

2 ))It is seen to double the power transfer to 2Pmax the required reactive power rating of SVC if 4 times the maximum power power transfer in an uncompensated cas, that is, 4Pmax.Such high rated SVCs may not be economcally feasible.

Enhancement of Transient Stability:

An SVC significantly enhances the ability to maintain synchronism of a power system, even when the system is subjected to large sudden disturbances.

An enhancement is transient stability is achieved primariliy through voltage control exercised by the SVC at the interconnected bus. Consider both the uncompensated and SVC compensated power system depicted in the figure.Assume that both the systems are transmitting the same level of power and are subject to an identical fault at the generator terminals for an equal length of time.The power angle curves in the uncompensated and compensated systems are indicated by rotor angle δ1 and δc1. These points corresponds to the intersection between respective power-angle curves with the mechanical input line Pm which is same for both the case.

Fig 5. Power angle curves depicting transient stability margins in the SMIB system (a) the uncompesated system (b) the SVC compensated system

In the event of a 3 phase to ground fault at the generator terminals, even though the short circuit current increase enormouslty, the active power output from the generator reduces to zero. Because the mechanical input remains unchanged, the generator accelerates until fault clearing, by which time the rotor angle has reached values δ2 and δc2 and the accelerating energy, A1 and Ac1 has been accumulated in the uncompensatd and compensated system, respectively. When the fault is isolated , the electrical power exceeds the mechanical inpur power and the generator starts decelarating. The rotor angle however continues to increase until δ3 and δc3 from the stored kinetic energy in the rotor. The decline in the rotor angle commences only when the decelarating energies represented by A2 and Ac2 in the two cases, respectively, become equal to the accelarating energies A1 and Ac1.

The power system in each case returns to stable operation if the post fault angular swing, denoted by δ3 and δc3, does not exceed the maximum limit of decelarate. The farther the angular overswing from its maximum limit, the more transient stability in the system. An index of the transient stability is the available decelerating energy, termed the transient stability margin, and is denoted by areas Amargin and Acmargin in the two cases respectively. Clearly, as Acmargin significantly exceeds Amargin the system transient stability is greatly enhanced by the installation of an SVC.

The increase in transient stability is thus obtained by the enhancement of the steady state power transfer limit provided by the voltage control operation of the midline SVC.

Mathematical Representation:

The above considered power system model without SVC can be represented in the mathematical equations in 4th order as:

d δdt

=wo ( w−1 )

d wdt

= 12H

∗( pm−pe )

d eq'

dt= 1

Tdo '∗( Efd−eq'−( xd '−xd ) id )

d⩟Efddt

=( KeTe )∗(uE+vtr−vt )−⩟Efd

Te

If the system is stable, there is no need of SVC to control the system. Hence, the susceptance of SVC will be zero initially. Now when a disturbance occurs in the system, SVC controller comes into picture and removes the oscillations after certain time interval.Now, Let us design a SVC model with a lead-lag compensator and develop the state equations from the model.

Fig 6. SVC with lead lag compensator

The figure above shows the lead lag compensator for SVC. The state equations for above system are:

dx5dt

=Ks (d ⩟wdt )− x 5

Tw

dx6dt

= x 5T 2

−( dx5

dt )T 1

T 2− x6

T 2

dx7dt

= x 6T 4

+( dx 6

dt )T 3

T 4− x 7

T 4

dBsvcdt

=Kc(x 7+Bsvcref )

Tc−Bsvc /Tc

Also we know that,

Pe=vd∗id+vq∗iq

Where,

vd=−ra∗id+xq∗iq

vq=−ra∗iq+eq '−xd '∗id

vt=v d2+v q2

The expressions for id and iq are obtained from solving the power system model.

Now, writing a program in MATLAB for the above power system we can obtain the results as:

SIMULATIONS AND RESULTS:

(a)

(b)

(c)

(d)

Fig 7. (a),(b),(c),(d)-Plots for uncompensated system for 4 cycles.

Simulation results with PSS:

Fig 8. Rotor angle and rotor speed vs time for 6 cycles with PSS

Conclusion:

In this study, the power system stability enhancement via PSS and SVC based stabilizer when applied independently and also through coordinated application was discussed and investigated. For the proposed stabilizer design problem, the mathematical model for the power system was developed . The model is most suitable for analysis and digital simulations of SVC in power systems. The proposed stabilizer have been tested on a weakly connected power system and non linear simulation results show the effectiveness and robustness of the proposed stabilizers to enhance the system stability.

References:

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2. Power System Dynamics Stability and Control by K.R. Padiyar

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FACTS: Concepts and technology of Facts

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