POWER SYSTEM STABILITY

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Contents

Power System Stability Overview Power System Stability: A Proposed Definition Need of Stability Classification Power System Stability Classification

Rotor Angle Stability Voltage Stability Frequency Stability

Rotor Angle Stability vs. Voltage Stability References

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Power System Stability Overview

Power system is defined as a network of one or more generating units, loads and power transmission lines including the associated equipments connected to it.

The stability of a power system is its ability to develop restoring forces equal to or greater than the disturbing forces to maintain the state of equilibrium.

Power system stability problem gets more pronounced in case of interconnection of large power networks.

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Power System Stability: A Proposed Definition

Power system stability is the ability of an electric power

system, for a given initial operating condition, to regain a

state of operating equilibrium after being subjected to a

physical disturbance, with most system variables bounded

so that practically the entire system remains intact.

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Need of Stability Classification

Stability analysis is easier. Also it leads to proper and effective understanding of different power system instabilities.

Key factors that leads to instability can be easily identified.

Methods can be devised for improving power system stability.

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Power System Stability Classification

Rotor angle stability. Small disturbance angle stability. Transient stability.

Voltage stability. Small disturbance voltage stability. Large disturbance voltage stability.

Frequency stability. Short term frequency stability. Long term frequency stability.

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Stability Classification at a Glance

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Rotor Angle Stability

Rotor angle stability refers to the ability of synchronous machines of an interconnected power system to remain in synchronism after being subjected to a disturbance.

Rotor angle instability occurs due to angular swings of some generators leading to their loss of synchronism with other generators.

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Rotor Angle Stability (contd.)

Depends on the ability to maintain/restore equilibrium between electromagnetic torque and mechanical torque of each synchronous machine.

At equilibrium, Input mechanical torque equals output electromagnetic torque of each generator. In case of any disturbance the above equality doesn’t hold leading to acceleration/ deceleration of rotors of machines.

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Rotor Angle Stability

Rotor Angle Stability Classification:

Small Disturbance Rotor Angle Stability:

It is the ability of the power system to maintain synchronism under small disturbances.

Disturbances are considered to be sufficiently small such that the linearization of system equations is permissible for purposes of analysis.

The time frame of interest in small-disturbance stability studies is of the order of 10 to 20 seconds following a disturbance.

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Rotor Angle Stability

Rotor Angle Stability Classification

Large Disturbance Rotor Angle Stability:

It is the ability of the power system to maintain synchronism under a severe disturbance, such as a short circuit on a transmission line.

Disturbances are large so that the linearization of system equations is not permissible for purposes of analysis.

The time frame of interest in small-disturbance stability studies is of the order of 3 to 5 seconds following a disturbance.

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Voltage Stability

Voltage stability refers to the ability of a power system to maintain steady voltages at all buses in the system after being subjected to a disturbance from a given initial operating condition.

A system is voltage instable if for atleast one bus in the system, the voltage magnitude decreases as reactive power injection is increased.

Voltage instability results in progressive fall or rise of voltages of some buses.

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Voltage Stability

Large scale effect of voltage instability leads to Voltage collapse. It is a process by which the sequence of events accompanying voltage instability leads to a blackout or abnormally low voltages in a significant part of the power system.

The driving force for voltage instability is usually the loads.

Voltage stability problems is also experienced at terminals of HVDC links connected to weak ac systems.

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Voltage Stability

Voltage Stability Classification

Small Disturbance Voltage Stability:

Small-disturbance voltage stability refers to the system’s ability to maintain steady voltages when subjected to small disturbances such as incremental changes in system load.

A combination of both linear and non-linear techniques are used for analysis.

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Voltage Stability

Voltage Stability Classification

Large Disturbance Voltage Stability:

Large-disturbance voltage stability refers to the system’s ability to maintain steady voltages following large disturbances such as system faults, loss of generation, or circuit contingencies.

The study period of interest may extend from a few seconds to tens of minutes.

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Frequency Stability

Frequency stability refers to the ability of a power system to maintain steady frequency following a severe system upset resulting in a significant imbalance between generation and load.

Frequency instability leads to tripping of generating units and/or loads.

Frequency stability may be a short-term phenomenon or a long-term phenomenon.

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Rotor Angle Stability vs. Voltage Stability

Rotor angle stability is basically a generator stability while voltage stability means load stability.

Rotor angle stability is mainly interlinked to real power transfer whereas voltage stability is mainly related to reactive power transfer.

A PRESENTATION ON REACTIVE POWER COMPENSATION

& VOLTAGE COLLAPSE

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Control of voltage and reactive power should satisfy the following

1.Voltages at the terminals of all equipment in the system are within acceptable limits

2. System stability is enhanced to maximize utilization of the transmission system. Voltage and reactive power control have a significant impact on system stability.

3. The reactive power flow is minimized so as to reduce RI2 and XI2 losses to a practical minimum. This ensures that the transmission system operates efficiently.

Since reactive power cannot be transmitted over long distances, voltage control has to be effected by using special devices dispersed throughout the system.

The proper selection and coordination of equipment for controlling reactive power and voltage are among the major challenges .

INTRODUCTION

Reactive power (VAR) compensation is defined as the management of reactive power to improve the performance of ac systems. There are two aspects:-

a) Load Compensation – The main objectives are to :-

i) increase the power factor of the system

ii) to balance the real power drawn from the system

iii) compensate voltage regulation

iv) to eliminate current harmonics.

b) Voltage Support – The main purpose is to decrease the voltage fluctuation at a given terminal of transmission line.

Therefore the VAR compensation improves the stability of ac system by increasing the maximum active power that can be transmitted.

WHAT IS REACTIVE POWER ?

Power is referred as the product of voltage and current

i.e. power = V x I The portion of electricity that establishes and sustains the

electric and magnetic fields of alternating-current equipment. Reactive power must be supplied to most types of magnetic equipment, such as motors and transformers.

In an ac transmission, when the voltage and current go up and down at the same time, only real power is transmitted and when there is a time shift between voltage and current both active and reactive power are transmitted.

WHY DO WE NEED REACTIVE POWER?

In resistive loads the current produces the heat energy which produces the desired output but incase of inductive loads the current creates the magnetic field which further produces the desired work. Therefore reactive power is the non working power caused by the magnetic current to operate and sustain magnetism in the device .

Reactive power (vars) is required to maintain the voltage to deliver active power (watts)through transmission lines. When there is not enough reactive power the voltage sags down and it is not possible to deliver the required power to load through the lines.

Need for Reactive Power Compensation

Reactive power generated by the ac power source is stored in a capacitor or a reactor during a quarter of a cycle and in the next quarter of the cycle it is sent back to the power source. Therefore the reactive power oscillates between the ac source and the capacitor or reactor at a frequency equals to two times the rated value (50 or 60 Hz). So to avoid the circulation between the load and source it needs to be compensated .

Also to regulate the power factor of the system and maintain the voltage stability we need to compensate reactive power .

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OBJECTIVES OF LOAD COMPENSATION

p.f. Correction. Voltage regulation improvement. Balancing of load

SPECIFICATIONS OF LOAD COMPENSATION

Maximum and continuous reactive power requirement in terms of absorbing as well as generation.

Overload rating and duration. Rated voltage and limits of voltage between which the

reactive power rating must not be exceeded. Frequency and its variation. Accuracy of voltage regulation requirement. Special control requirement. Maximum harmonic distortion with compensation in series. Emergency procedure and precautions. Response time of the compensator for a specified

disturbance. Reliability and redundancy of components.

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IDEAL COMPENSATOR

An ideal compensator is a device that can be connected at or near a supply

point and in parallel with the load. The main functions of an ideal

compensator are instantaneous p.f. correction to unity, elimination or

reduction of the voltage regulation, and phase balance of the load currents

and voltages. In performing these interdependent functions, it will consume

zero power.

The characteristics of an ideal compensator are to:

provide a controllable and variable amount of reactive power

without any delay according to the requirements of the load,

maintain a constant-voltage characteristic at its terminals, and

should operate independently in the three phases

Methods of Reactive Power Compensation

Shunt compensation Series compensation Synchronous condensers Static VAR compensators Static compensators

Shunt compensation

The device that is connected in parallel with the transmission line is called the shunt compensator. A shunt compensator is always connected in the middle of the transmission line. It can be provided by either a current source, voltage source or a capacitor.

An ideal shunt compensator provides the reactive power to the system.

Shunt-connected reactors are used to reduce the line over-voltages by consuming the reactive power, while shunt-connected capacitors are used to maintain the voltage levels by compensating the reactive power to transmission line.

Transmission line with shunt compensation

Series compensation

When a device is connected in series with the transmission line it is called a series compensator. A series compensator can be connected anywhere in the line.

There are two modes of operation – capacitive mode of operation and inductive mode of operation.

A simplified model of a transmission system with series compensation is shown in Figure .The voltage magnitudes of the two buses are assumed equal as V, and the phase angle between them is δ.

Transmission line with series compensation

Static VAR compensators

A static VAR compensator (or SVC) is an electrical device for providing  reactive power on transmission networks. The term "static" refers to the fact that the SVC has no moving parts (other than circuit breakers and disconnects, which do not move under normal SVC operation).

The SVC is an automated 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 (usually in the form of thyristor-Controlled Reactors) to consume vars from the system, lowering the system voltage.

Under inductive (lagging) conditions, the capacitor banks are automatically switched in, thus providing a higher system voltage.

ADVANTAGES

a) Static VAR compensation is not done at line voltage; a bank of transformers steps the transmission voltage (for example, 230 kV) down to a much lower level (for example, 9.5 kV).This reduces the size and number of components.

b) They are more reliable .

c) Faster in operation .

d) Smoother control and more flexibility can be provided with the help of thyristors.

Static Compensator

 The devices use synchronous voltage sources for generating or absorbing reactive power. A synchronous voltage source (SVS) is constructed using a voltage source converter (VSC). Such a shunt compensating device is called static compensator or STATCOM .

A STATCOM usually contains an SVS that is driven from a dc storage capacitor and the SVS is connected to the ac system bus through an interface transformer. The transformer steps the ac system voltage down such that the voltage rating of the SVS switches are within specified limit.

Structure of STATCOM

Basically, the STATCOM system is comprised of

Power converters,

Set of coupling reactors or a step-up transformer,

Controller

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COMPARISON OF VI CHARACTERISTICS OF SVC AND

STATCOM

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Advantages of STATCOM

The reactive components used in the STATCOM are much smaller than those in the SVC.

The characteristics of STATCOM are superior. The output current of STATCOM can be controlled up to

the rated maximum capacitive or inductive range. Reduction of the capacity of semiconductor power

converter and capacitor bank to one half of those for the conventional SVC.

Better transient response of the order of quarter cycle. Reduction of harmonic filter capacity. Reduction of size of high value air-cored reactor. Reduction of equipment volume and foot-print.

Synchronous Condensor

A device whose main function is the improvement of pf of the electrical system is known as the synchronous condensor. It is installed at the receiving end of the line .

When a synchronous condensor is introduced it supplies the kVAR to the system , and hence the current is reduced .

Therefore the losses are reduced and provides a better efficiency . Hence more power can be delivered to the load and improves the pf of the system.

CONCLUSION

From all the previous discussion we can conclude reactive power compensation is a must for improving the performance of the ac system. By reactive power compensation we can control the power factor and reduce the consumption of electricity.

METHODS OF VOLTAGE CONTROL

The different voltage-control methods are:

Excitation control. Shunt capacitors. Series capacitors. Tap-changing transformers. Boosters. Synchronous condensers

Excitation control:

 This method is used only at the generating station.

Due to the voltage drop in the synchronous reactance of armature, whenever the load on the supply system changes, the terminal voltage of the alternator also changes.

This can be kept constant by changing the field current of the alternator according to the changes in load. This is known as excitation control.

Shunt capacitor Series capacitor

1. Supplies fixed amount of reactive power to the system at the point where they are installed. Its effect is felt in the circuit from the location towards supply source only

1. Quantum of compensation is independent of load current and instantaneous changes occur. Its effect is from its location towards the load end

2. It reduces the reactive power fl owing in the line and causes:

a. Improvement of p.f. of a systemb. Voltage profile improvementc. Decreases kVA loading on source,

i.e., generators, transformers, and line upto location and thus provides an additional capacity

2. It is effective:

a. On tie lines, the power transfer is greater

b. Specifically, suitable for situations when flickers due to respective load functions occur

3. The location has to be as near to the load point as possible. In practice, due to the high compensation required, it is found to be economical to provide group compensation on lines and sub-stations

3. As a thumb rule, the best location is 1/3rd of electrical impedance from the source bus

4. As fixed kVAr is supplied, this may sometimes result in overcompensation in the light-load period. Switched kVAr banks are comparatively costlier than fixed kVAr and become necessary

4. As full-load current is to pass through, the capacity (current rating) should be more than the load current

5. As the p.f. approaches unity, larger compensation is required for the improvement of p.f.

5. As series capacitors carry fault current, special protection is required to protect from fault current

6. Where lines are heavily loaded, compensation required will be more

6. Causes sudden rises in voltage at the location

7. Cost of compensation is lower than that of the cost required for series capacitor

7. Cost of a series capacitor is higher than that of a shunt capacitor

Series Capacitor

Series Capacitor

Tap-changing transformers

A tap-changing transformer is a static device having a number of tap settings on its secondary side for obtaining different secondary voltages.

The basic function of this device is to change the transformation ratio, whereby the voltage in the secondary circuit is varied making possible voltage control at all voltage levels at any load.

The supply may not be interrupted when tap changing is done with and without load.

Off-load tap-changing transformers The off-load tap-changing transformer, which requires

the disconnection of the transformer from the load when the tap setting is to be changed

The output of the secondary side of the transformer changes with the change in the tap position of the secondary winding. The secondary voltage is minimum when the movable arm makes contact with stud 1, whereas it is maximum when it is in position N. When the load on the transformer increases, the voltage across secondary terminals decreases. This can be increased to the desired value by adding the number of turns on the secondary of the transformer by changing taps.

The main drawback is that the taps are changed only after the removal of the load. This can be overcome by using an on-load tap-

changing transformer with reactors.

On-load tap-changing transformer To supply uninterrupted power to the load (consumer), tap changing has to

be performed when the system is on load. The secondary winding in a tap-changing transformer consists of two

identical parallel windings with similar tappings. For example, 1, 2, …, N and 1′, 2′, …, N′ are the tappings on both the parallel windings of such a transformer. These two parallel windings are controlled by switches Sa and Sb as shown in Fig.

In the normal operating conditions, switches Sa, Sb, and tappings 1 and 1′ are closed, i.e., both the secondary windings of the transformer are connected in parallel, and each winding carries half of the total load current by an equal sharing.

The secondary side of the transformer is at a rated voltage under no load, when the switches Sa and Sb are closed and movable arms make contact with stud 1 and 1′, whereas it is maximum (above the rated value) under no load, when the movable arms are in position N and N′. The voltage at the secondary terminal decreases with an increase in the load. To compensate for the decreased voltages, it is required to change switches from positions 1 and 1′ to positions 2 and 2′ (number of turns on the secondary is increased).

For this, open any one of the switches Sa and Sb, assuming that Sa is opened. At this instant, the secondary winding controlled by switch Sb carries full-load current through one winding. Then, the tapping is changed to position 2 on the winding of the disconnected transformer and close the switch Sa. After this, switch Sb is opened for disconnecting its winding, and change the tapping position from 1′ to 2′ and then switch Sb is closed. Similarly, tapping positions can be changed without interrupting the power supply to the consumers.

This method has the following disadvantages:It requires two windings with rated current-carrying capacity instead of one winding.It requires two operations for the change of a single step.Complications are introduced in the design in order to obtain a high reactance between the parallel windings.

Booster transformers

The booster transformer performs the function of boosting the voltage. It can be installed at a sub-station or at any intermediate point of line.

Synchronous condenser Static capacitors

1. Harmonics in the voltage does not exist 1. Large harmonics are produced in the system

2. Power factor variation is stepless (uniform)

2. Power factor varies in steps

3. It allows overloading for a short period 3. It does not allow any overloading

4. Power loss is more 4. Power loss is less

5. It is more economical in the case of large kVAr

5. It is more economical for small kVAr requirement

6. Failure rate is less and, therefore, this is more reliable

6. Failure rate is more and, therefore, it is less reliable

PV CURVES

The conceptual analysis of voltage stability is useful carried out by using P–V curves. These are useful for the study of analysis of radial systems.

The short-circuit current,  Short-circuit p.f.,  The total load current,

The power delivered to the load,

Condition for maximum power delivered is 

∴ RL = Z, is the condition for maximum power deliveredSubstituting this condition in Equation (9.42), we get the maximum

power as

Now Voc is the open-circuit voltage, i.e., Vr when Ir = 0.

Let x be the distance from the sending end and l be the length of the line

For a lossless line, r = 0 and g = 0, then the voltage at distance x from the sending end becomes

V(x) = Vr cos β(l − x) + jZcIr sin β(l − x) where β is the phase constant Suppose the line is open circuited at the receiving

end, i.e., Ir = 0,

Similarly, the short-circuit current Isc is the value of Ir when Vr = 0

Assuming the line to be lossless, cos ϕsc = 0

Equation (9.43) represents loci of maximum power for different line lengths at unity p.f.

The receiving-end current, 

The sending-end voltage of the line, if assuming the line to be lossless, now becomes

For a fixed sending-end voltage Vs and the fixed line length, Equation (9.44) is quadratic in Vr and thus will have two roots. Figure 9.25 shows a graphical relation between   as a function of normalized loading  .

From Fig. 9.25, it is observed that the maximum power can be transmitted for each load p.f. and for any loading, there are two different values of Vr.

The normal operation of the power system is along the upper part of the curve where the receiving-end voltage is nearly 1.0 p.u.

The load is increased by decreasing the effective resistance of the load upto the maximum power; the product of load voltage and current increases as the system is stable.

As the point of maximum power is reached, a further reduction in effective load resistance reduces the voltage more than the increase in current and therefore, there is an effective reduction in power transmission.

The voltage finally collapses to zero and the system at the receiving end is effectively short-circuited and therefore, the power transmitted is zero (point at origin in Fig. 9.25).

It is observed from Fig. 9.25 that the power transmitted is zero both at Point K and Point 0. Point K corresponding to the open circuit and Point 0 corresponding to the short circuit and in either case the power transmitted is zero.

These P–V curves are different for different p.f.’s. At more leading p.f.’s, the maximum power is higher and for that the shunt compensation is provided.

The nose voltage of the P–V curve has the critical voltage at the receiving end for maximum power transfer.

With leading p.f., the critical voltage is higher, which is a very important aspect of voltage stability.

QV CURVES

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