VOLTAGE STABILITY

Souvik Khan

Pujan Narjinary

What is Voltage Stability?

Voltage stability is ability of a power system to maintain acceptable voltages at all buses in the system under normal operating condition after being subjected to a disturbance

What is Voltage instability?A Power system enters a state of voltage instability when

• A disturbance,• An increase in load demand, or • A change in system condition causes progressive and uncontrollable voltage drop.

Main cause :• Inability of the power system to meet the demand for reactive

power

Considering the characteristics of a transmission system, generators, loads and compensating devices we can better understand the phenomenon.

Characteristics of transmission system

A two terminal network can demonstrate voltage stability’s simplest form. It represents a simple radial system. • a constant voltage source (Es),• a load (Zld) and • a series impedance (Zln).

Current

Considering normalized values of I, and tanθ =10 and cos Φ =0.95

RV

RP

Fig. 1

• The load impedance is decreased to increase load demand, increases rapidly at first and then decreases after reaching a point of maximum power .

• Maximum power occurs only when is equal to the voltage drop in the line, i.ewhen =1.

• The operating condition at maximum power represents the limit for satisfactory operation.

• Upon higher load demand the control of power cannot be done by altering load impedance as lowering load impedance causes power to decrease. Depending upon the load characteristics the voltage will progressively decrease and the system will become unstable .

𝐼= 1√ 𝐹

𝐸𝑠

𝑍𝐿𝑁𝑉=

𝑍 𝐿𝐷𝐸𝑆

√ 𝐹 𝑍 𝐿𝑁❑𝑃= 1

√𝐹 ( 𝐸𝑠❑

𝑍𝐿𝑁)

2

𝑍𝐿𝐷cos∅

2

𝑍 𝐿𝐷

Where

• With a constant impedance static load characteristics, the system stabilizes at power and voltage levels below desired values

• With a constant power load characteristics, the system becomes unstable through load bus voltage collapse

• With other characteristic the voltage is determined by composite characteristic of the transmission line and load. If the load is supplied with power through a ULTC(Under Load Tap Changer) it will attempt to increase the voltage, which results in reduction of effective load impedance .This causes further progressive reduction in and finally enters a state of voltage instability.

Fig. 3

The above figure shows the relationship between and ,for a constant source voltage and taking different values of power factor. Operating points above the critical points represent satisfactory operating conditions

𝐸𝑆

RQ

Fig. 4The above figure represents characteristics of a simple radial

system with different ratio. • The system is stable in region where the derivative is positive. • The voltage stability limit is reached when the derivative reaches

zero.• The QV curve at the right side represent stable operation and to the

left is the unstable operation

Generator characteristics :

• Generator AVRs are the most important means of voltage control in a power system.

• During low voltage conditions, the reactive power demand on the generator increases but due to the field current limit and/or armature current limit, maintaining constant terminal voltage is not possible.

• With constant field current, the point of constant voltage is behind the synchronous reactance which increases the network reactance noticeably causing voltage collapse.

To show the impact of loss of generator voltage control capability consider the system shown consisting of a large load, an infinite bus and a generator regulating voltage .

• With voltage maintained at the bus, the V-P characteristics is shown by curve 1.

• When the field current limit is hit the bus voltage is no longer maintained and V-P characteristics follows curve 2.

• Point A on curve 1 represents a more stable operating condition than it on curve 2.

Impact of loss of regulation of intermediate bus voltage

LOAD Characteristics:

• Load characteristics have an important influence on system stability since stable operation of a power system depends on the ability to continuously match the electrical output of generating units to the electrical load on the system.

• In power system stability and power flow studies, a load model is used to represent the composite load characteristics as seen from bulk power delivery points.

• Load modelling is categorized into static models and dynamic models.

• A static load model expresses the characteristics of the load at any instant of time as algebraic functions of the bus voltage magnitude and frequency at that instant .

• A dynamic load model is required for systems where the amplitudes of voltage/frequency change is large. Its needed for the study of voltage stability and long term stability, and for systems with large concentrations of motors.

Static model :• traditionally, the exponential model represents the voltage

dependancy of load characteristics,

where a & b are the load parameters,

, initial active power,

, initial reactive power and

• Alternatively, a polynomial model is widely used

this model is also referred to as the ZIP model.

Dynamic Model:

• Since 60 to 70% of total energy is absorbed by the motors, therefore the dynamics attributable to motors are the most significant aspects of dynamic characteristics of system loads.

Other aspects are • discharge lamps below certain voltage goes off and restarts

after voltage recovers thus there is few seconds delay.• operation of protective relays(thermal & overcurrent).Many

industrial motors have starters with electromagnetically held contactors which open at voltages 0.55 to 0.75 pu dropout time is of the order of few cycles . Small motors on refrigerators or air conditions have thermal overload protection which trip at about 10 to 30 sec.

• thermostatic control of loads such as coolers, heaters, refrigerators etc.

• response of ULTCs on Distribution transformers, voltage regulators and voltage controlled capacitor banks.

Characteristics of reactive compensating devices :

• Let us take an example of an long transmission high voltage line supplying a radial load from a strong system as shown.

• The Q-V curves with sending end voltage constant, for four different values of receiving end load at unity p.f combined with Q-V characteristics of shunt capacitor for different four reactive power injections follows

System and shunt capacitors steady state Q-V characteristics, capacitors MVAr shown at rated voltage

16

CAUSES OF VOLTAGE COLLAPSE

the load on the transmission lines is too high. the voltage sources are too far from the load centres. the source voltages are too low. large distances between generation and load. ULTC action during low voltage conditions. poor co-ordination between various control and

protective systems. insufficient load reactive compensation.

SIMULATION OF VOLTAGE COLLAPSE The following slides simulate a voltage collapse in a simple power system. The West

generator has unlimited VAR (or reactive power) supply capability so it is able to keep the voltage at its bus constant at 1.0 per unit (or at the rated voltage). The East generator can only supply up to 1,200 MVARs (or 1,200 million VARs). There are 6,000 MWs of real power load and 1,000 MVARs of reactive power load at each bus. The West generator is transferring 3,000 MW to the East to help serve the 6,000 MW load in the East. Therefore, the outputs of the West and East generators are 9,000 MW and 3,000 MW respectively.

Six identical lines are initially in service and the 3,000 MWs of real power transfer are divided equally across the lines. The generators in the West and East are supplying reactive power (or VARs) to their local loads plus VARs to the transmission lines to support the transfer. The lines are assumed to be lossless (that is, they do not absorb real power). We have assumed that the individual line capacities (or thermal ratings) exceed 3,000 MW so the real power transfer could occur on one line if maintaining voltage (through sufficient VAR supply) is not a problem. Circuit breakers can open (or trip) the lines.

Symbols in the Simulation Window

• Buses: heavy dark lines (East and West) where the generators, loads and transmission lines interconnect

• Transmission lines: lines connecting the two buses

• Generators: circles with “dog bone rotors”

• Loads: arrows connected to the buses

• Circuit breakers: red boxes

• Line flows: arrows on the transmission lines (more easily seen in the last three simulations that follow) indicate the direction and magnitude of power flow

Simulating an AC System Voltage Collapse

Suppose the lines fail (that is, trip out) one at a time for any reason.

Case 1: No Lines Out. Bus voltages at 1.0 per unit (or rated voltage). Both bus voltages are being controlled by their respective generator VAR supplies.

Case 2: One Line Out. Bus voltages at 1.0 per unit (or rated voltage). Both bus voltages are being controlled by their respective generator VAR supplies.

Case 3: Two Lines Out. Bus voltages at 1.0 per unit (or rated voltage). Both bus voltages are being controlled by their respective generator VAR supplies although the East generator has just hit its VAR limit.

Case 4: Three Lines Out. East bus voltage at 0.99 per unit because East generation is at its reactive power supply limit. West generation still has unlimited reactive power supply capability.

Case 5: Four Lines Out. East bus voltage drops to 0.97 per unit. East generation at its reactive power supply limit. West reactive power generation continuing to rise.

Case 6: Voltage collapse! With five lines out, the simulation fails – which indicates that it is not possible to transfer 3,000 MW without additional reactive power support in the East even if West generation has excess reactive power supply capacity!

EastWest

1.00 PU

6000 MW

1000 MVR

1.00 PU

1150 MVR9000 MW

1150 MVR

3000 MW

6000 MW

1000 MVR

Case 1: All Lines In-Service

3,000 MW transfer – 500 MW per line

Voltage is 100% of rated voltage.

(300 MVARs required by lines).

East generator is below 1,200 MVAR

limit.20

EastWest

1.00 PU

6000 MW

1000 MVR

1.00 PU

1176 MVR9000 MW

1186 MVR

3000 MW

6000 MW

1000 MVR

Case 2: One Line Out

3,000 MW transfer – 600 MW per line

Voltage is 100% of rated voltage

(362 MVARs required by lines).

East generator is below 1,200 MVAR limit.

21

EastWest

1.00 PU

6000 MW

1000 MVR

1.00 PU

1253 MVR9000 MW

1200 MVR

3000 MW

6000 MW

1000 MVR

Voltage is 100% of rated (453 MVARs required by lines).

East generator is at 1,200 MVAR limit.

Case 3: Two Lines Out

3,000 MW transfer – 750 MW per line

22

EastWest

0.99 PU

6000 MW

1000 MVR

1.00 PU

1411 MVR9000 MW

1200 MVR

3000 MW

6000 MW

1000 MVR

Voltage is only 99% of rated (611 MVARs required by lines).

East generator is at 1,200 MVAR limit.

Case 4: Three Lines Out

3,000 MW transfer – 1,000 MW per line

23

EastWest

0.97 PU

6000 MW

1000 MVR

1.00 PU

1757 MVR9000 MW

1200 MVR

3000 MW

6000 MW

1000 MVR

Voltage has dropped to 97% of rated voltage(957 MVARs required by lines).

East generator is at 1,200 MVAR limit.

Case 5: Four Lines Out

3,000 MW transfer – 1, 500 MW per line

24

EastWest

0.77 PU

6000 MW

1000 MVR

1.00 PU

3500 MVR8926 MW

1200 MVR

3000 MW

6000 MW

1000 MVR

This simulation could not solve the case of 3,000 MW transfer with five lines out. Numbers shown are from the model’s last attempt to solve. The West generator’s unlimited supply of VARs is still not sufficient to maintain the voltage at the East bus.

Case 6: Five Lines Out

Voltage Collapse

25

26

PREVENTION OF VOLTAGE COLLAPSE

application of reactive power compensating devices control of network voltage and generator reactive o/p co-ordination of protection / controls control of transformer tap changers

Scenario of classic voltage collapse

1. Some EHV transmission lines are heavily loaded, the available generation capacity of the critical area is temporarily reduced e.g. due to maintenance of unit or to market conditions, and reactive power reserves are at the minimum or are located far from the critical area.

2. Due to a fault or any other reason a heavily loaded line is lost. The loading and reactive power losses of remaining lines increase. The total reactive power demand increases due to these reasons.

Scenario of classic voltage collapse 3. The load voltage decreases, which in turn decreases the load

demand and the loading of EHV transmission lines. The voltage control of the system, however, quickly restores generator terminal voltages by increasing excitation. The additional reactive power flow at the transformers and transmission lines causes additional voltage drop at these components.

4. After a few minutes (depending on the time delays of on-load tap changers) the on-load tap changers of distribution substation transformers restore the distribution network voltages. The increased voltage also increases the load demand. The EHV transmission line losses increase, which causes greater voltage drop at these lines.

Scenario of classic voltage collapse 5. The increased reactive power demand increases the

reactive output of the generators. When the generator hits the reactive power limit, its terminal voltage decreases. Its share of reactive power demand is shifted to another generator further away from the critical area. This will lead to cascading overloading of generators. Fewer generators are available for voltage control and they are located far from the critical area. The decreased voltage at the transmission system reduces the effectiveness of shunt capacitors. The system becomes prone to voltage instability, which may lead to voltage collapse.

Voltage Collapse History

1. France 19782. Belgium 19823. Florida USA 19854. Western France 19875. Southern Finland August 19926. WSCC USA July 2 1996