1. Reactive power compensation and dynamic performance of transmission systems
Presented by,
Sudarshan B S
Asst. Professor
Dept. of EEE
RVCE, Bangalore

2. Introduction
For smooth working of a complex power system network, it is important to ensure the network be in steady state.
A power system is said to be in steady state if the state variables of the power system do not change with respect to time. Mathematically it means that the time rate of change of the state variable is zero.
Can a power system be in steady state for a long time ?
NO!!!!
Changes and disturbances in power system usually cause the power system to come out of steady state. Once the disturbance is cleared, the system settles at a new steady state operational point. In other words, a power system is almost always in a state of transition between steady state conditions.

3. Dynamic Phenomena in Power Systems

4. Need for Adjustable Reactive Compensation
There are three major reasons that support the need for adjustable reactive power compensation. They are:
The need to maintain the stability of synchronous machines
The need to control voltage
To prevent unnecessary flow of reactive power.

5. Need for Adjustable Reactive Compensation
The need to maintain the stability of synchronous machines
Disturbances cause rapid change in synchronous machine power angle.
Voltage control by reactive power compensation can have a positive stabilizing effect on the system in times of disturbances which cause the synchronous machine power angle to change rapidly.
It is possible to enhance both transient and dynamic stability of a system.
With the help of controlled compensators, we can also drive the voltages deliberately out of their normal steady-state bounds for several seconds after a disturbance to enhance the stabilizing influence still further.

6. Need for Adjustable Reactive Compensation
The need to control voltage
Consumer loads need quality power supply. This includes maintaining the voltage within acceptable limits around the steady-state value.
Following disturbances, voltage deviations occur.
If the voltage deviations are not corrected, they may lead to outage or damage to the utility or the consumer equipment.
Even small voltage variations beyond the acceptable limits is objectionable.
Following abrupt changes in loads or during changes in network configuration due to switching of power electronic switches, voltage correction for a few cycles of power frequency will be sufficient.
For some voltage deviations, it is necessary to provide a corrective action for a few seconds.

7. Need for Adjustable Reactive Compensation
To prevent unnecessary flow of reactive power.
There is a need to regulate the voltage profiles in the network to prevent unnecessary flow of reactive power on transmission lines.
Reactive power compensation is used to maintain losses at the minimum.
Although the compensation must be adjusted to keep the losses minimum, the adjustments can be made infrequently.

8. Four Characteristic Time Periods
The transition period between any two equilibria is divided into four characteristic time periods.
This helps in clearly understanding and describing the influence of the compensating methods on system dynamic performance.
These time periods are not defined based on duration, rather on the events and processes taking place within them.
The four distinct time periods are:
Sub-transient period
Transient period
First-swing period
Oscillatory period
Consider a disturbance in a power system.

9. Sub-Transient & Transient Periods

10. aC & DC components of Fault Current
Initially, we assume that the pre-fault current is zero.
When a short-circuit occurs, the current changes over time from the initial value (zero) to the value that would exist under short-circuit conditions.
This value is the “symmetrical current,” also referred to as the “ac component” of the short-circuit current.
In the ideal case, where the circuit resistance is zero and the current is limited only by the circuit inductance, the short-circuit current and the system voltage would be out of phase by 90°.
Thus, the worst-case instant for initiating the short-circuit current would be when the system voltage is zero.

11. aC & DC components of Fault Current
In the real world, the circuit resistance is non-zero. Thus, the worst case does not occur when the system voltage is zero. Rather, it occurs a few degrees from zero voltage, but we’ll ignore that nicety* in this discussion.
By definition, the short-circuit current is limited only by the circuit inductance.
The current in an inductor cannot change instantaneously from the initial value (zero) to the short circuit value.
To achieve a current balance at the instant of short circuit initiation, we consider that the short-circuit current consists of an ac component (the symmetrical component) and a dc component, which accounts for the difference between the steady-state short-circuit current at the instant of fault initiation and the initial zero value.
The dc component must be equal in magnitude to the instantaneous value of the symmetrical steady-state current at time 0.
The dc component of the short-circuit declines exponentially from the initial value, with a time constant that is determined by the values of the circuit inductance (X) and resistance (R).
Nicety = A fine or subtle detail or distinction

12. Sub-Transient Period
The first several cycles following a disturbance is called the sub-transient period.
During this period there is an initial rapid decay of both ac and dc components of fault current.
These components not only include power frequency components but sometimes also include high-frequency components which are rapidly damped.
Power system components such as surge arresters, spark gaps and non-linear reactors (including transformer- magnetizing reactance) act during this period to prevent extreme voltages that cause insulation failure.

13. Transient Period The next in sequence is the transient period.
It lasts for many cycles after sub-transient period.
During this time, synchronous machines are modelled as an emf behind a constant reactance, the transient reactance Xd’. Usually we take Xd’ = {Xl + (Xf || Xa)}
During this period, it can be assumed that no appreciable changes occur in rotor angles of synchronous machines.

14. What Happens After Transient Period???
The disturbances in power systems may be,
very small
very distant (electrically) from the generators
In the first case, the disturbance does not cause any significant change in rotor angles of synchronous machine. In the second case, the changes in rotor angles can be neglected even for large disturbances.
In such cases the total time (sub transient + transient) is referred to as the transition time.
However, if at the point of interest the rotor angle difference is not negligible and is significant then the total transition period can be subdivided into sub-transient, first swing, and oscillatory periods

15. Sub-Transient, First Swing & Oscillatory Periods

16. First Swing Period
The first-swing period refers to the time for the first swing (half oscillation) of the rotor angle(s) or synchronizing power swings following a large disturbance, such as a fault.
This period typically lasts for about 0.5 to 1 second.
In this period, synchronous machines may be approximately characterized by constant internal source voltage behind the machine’s transient reactance.
This period is very important as it represents the time period during which the transient stability is maintained or lost.

17. Oscillatory Period & Quasi-State Period
The oscillatory period comes after the first-swing period.
During this period, significant cyclic variations in voltages, currents, and real and reactive power take place.
Synchronizing power swings caused by synchronous machine rotor angle swings may lost for 3-20 seconds after a severe fault.
The exact time depends on the damping provided by the excitation controls and amortisseur currents in synchronous machines, speed governor control on turbines, and the loads.
Note:
Amortisseur winding is a squirrel cage winding placed near the surface of the pole faces of a synchronous motor. Its main purpose is to dampen any speed fluctuations or oscillations that may occur as a result of sudden load changes. It is also used to accelerate the motor during starting. All the windings are shorted at the two ends of each pole of the motor. As the rotating field moves past the winding it induces currents in the winding which produce torque and accelerate the motor so as to overcome the lag in its speed.
The final period is the quasi-state period. It is reached when the synchronizing power and rotor angle swings have died out.

18. Can We Represent Using Phasors???
Immediately after occurrence of a disturbance, the voltages and currents in a power system are not pure sine waves. They include,
dc offset currents
unbalance between phases
harmonics, when nonlinear circuit elements are involved
Hence, it is not completely correct to visualize the response mechanisms are phasors.
Although the phasor representation gives a fair idea, field tests, computer simulations and modelling on transient network analysers are better suited to understand the responses.
The compensation methods which are of interest here are designed to be effective in the transient and the following periods. Hence, for the sake of analysis, it is acceptable to skip the sub-transient state. The sub-transient period is too small for the reactive power compensation to be effective.

19. Example – Two Machine System
Consider a two-machine system shown here. The system is assumed to lossless and the line capacitance is ignored.
The intermediate substation is assumed equidistant from sending and receiving ends. The reactances are chosen so that the system is electrically symmetric around this bus.

20. Example – Two Machine System - Line Removal, No Fault
Vm → the voltage on the midpoint bus
|E1’| = |Er|
The only load in the system is in the receiving end.
The sending end generator is delivering power to the receiving end system.
In steady state, let the sending end generator deliver power and the corresponding current be I1.
The phasor representation for such a system is shown here.
The subscript 1 represents the case-1 (the steady-state)

21. Example – Two Machine System - Line Removal, No Fault
Let breakers ‘a’ and ‘b’ be opened simultaneously to disconnect the transmission line. When this happens, the phasor diagram changes to the new phasors as shown here.
In this new condition, all phasors are represented using subscript 2.
Note that the total angle δ1 remains fixed. This is because the angle are fixed to inertial rotating phasors. These phasors cannot change their speed instantaneously. Hence δ1 does not change.

22. Example – Two Machine System - Line Removal, No Fault
At the instant of opening breakers, the two voltages E1’ and Er are momentarily fixed in magnitude and are displaced by a (momentarily) fixed angle. Therefore the sum of voltage drops across the system remains the same.
However, when the line is removed, the equivalent reactance between the sending end bus and the mid-station bus has now increased to Xl (from Xl/2 before fault). This leads to a reduction in current from I1 to I2.
All bus voltages are instantly phase shifted relative to each other and the source voltages E1’ and Er.
The magnitudes of the bus voltages increase momentarily during the transient period. If both source voltages were to remain fixed in relative phase and fixed in magnitude, the transition period would be complete and this phasor would represent the new steady state.

23. Example – Two Machine System - Line Removal, No Fault
Assume,
the receiving end system is so large in MVA capacity that Er is essentially constant in magnitude and rotates continuously at a constant synchronous speed [Ns = (120f/p) rpm]
The phasor E1’, on the other hand, is associated with a generator unit of finite capacity.
that the mechanical power delivered by the sending end turbine to the generator shaft (mechanical input to the generator) is constant

24. Example – Two Machine System - Line Removal, No Fault
The reduction in current from I1 to I2 implies a reduction in power output of the sending-end generator.
As per our assumption, the turbine gives constant mechanical power. This means there is a momentary mismatch between the input power (from turbine) and the output power (from the generator). This mismatch causes the turbine-generator unit to accelerate.
During this acceleration period, the angle δ1 becomes larger.

25. Example – Two Machine System - Line Removal, No Fault
This is a momentary large disturbance and causes the generator unit to change speed.
Now the transient state will be followed by the first swing and oscillatory periods.
Now that δ1 has increased, the phasor E1’ will rotate (to reflect increase in δ1) and it will settle at a large angle that corresponds to the initial active power delivered by the sending end generator.
The voltage magnitudes Vs, Vm and Vr will be changed back toward their initial values by the unit’s voltage regulation action.

26. Example – Two Machine System - Line Removal After Fault
Let us assume that a short-circuit fault had occurred before the line outage and then the breakers tripped.
In such a case, the unit’s acceleration would be greater than that caused by manually opening the breakers without fault.
This would cause a much higher increase in δ and the transient angular momentum is redistributed.
This distribution, if not limited, will cause a loss of synchronism.
The initial conditions remain the same and hence the same phasor is valid for initial conditions (slide #20).
The phasor, for the case with fault, is shown in this slide.

27. Example – Two Machine System - Line Removal After Fault
Curve-2 represents the power vs. angle condition for the initial conditions (before occurrence of fault).
After the fault has occurred and the breakers have been opened, the power vs. angle curve changes to the curve represented by 1.
Point-A represents the operating point during the initial conditions. Here, δ=δ1.
Point-B represents the final operating point corresponding to δ=δ2.
Power vs. Angle Curves: 2=before disturbance; 1=after line section is disconnected; A=initial operating point; B=final operating point.

28. Example – Two Machine System - Line Removal After Fault
Figure here shows the machine load angle δ, the electrical power P, and the mid-system bus voltage Vm for the entire scenario (including the fault and first swing periods).
As the power P increases (fault occurrence), the voltage Vm drops to a minimum value at t = tp. There exists a large voltage variation in this period. Hence dynamic reactive power compensation at mid-system bus is necessary to minimize the voltage variations.

29. Example – Two Machine System - Line Removal After Fault
The dynamic reactive power compensation at bus m has a positive effect on the voltage and power angle swings. This is shown in figure here.
In most cases, a synchronous condenser or a static compensator is used for dynamic compensation.
The voltage support provided by these compensators tend to reduce the transmission angle variations.
In some cases, they also help maintain the transient stability of the system.
Solid line = uncompensated system
Dashed line = compensated system

30. Example – Two Machine System - Line Removal After Fault
The most important difference in the processes occurring in the first swing period from that in transient period is that the internal voltage E’ may increase in the first swing as a result of rapidly increasing field current forced by the exciter.
This tends to increase the power transfer capability of the generator and transmission system at any given δ.
This in turn results in reduction of first-swing angular excursion during the post-disturbance synchronizing power swings.

31. Example – Two Machine System - Line Removal After Fault
The third characteristic period after the disturbance has occurred is known as the oscillatory period. It is the period between the first swing in the synchronizing power (and machine rotor angle) and the time a which quasi- steady state is reached.
Depending on the system, the oscillations may or may not damp out. The damping out takes anywhere between 2 and 20 seconds.
In some cases, ‘negative damping’ influences become higher, causing the oscillations to grow until one or more generator loses synchronism. This is sometimes called ‘dynamic instability.’ This is common in systems where power is transmitted for very long distances.
For maintaining the transient stability in generators of such systems, fast-response, high-gain excitation systems are employed.

32. Example – Two Machine System - Line Removal After Fault
For maintaining the transient stability in generators of such systems, fast-response, high-gain excitation systems are employed.
In addition, supplementary stabilizer systems may also be used as the high field time constants contribute to the instability.
These stabilizers sense the oscillation in rotor speed, deviations in bus frequency, or power, and modulate the voltage regulator reference in the excitation controller to damp out the oscillation.
By modulating the reactive power flows in the system, compensators can exert a significant positive damping influence.

33. Example – Two Machine System - Line Removal After Fault
Effect of daily load cycle
At the end of oscillatory period, the system reaches steady state. However, the system does not stay in that state for a long time. Even if no major disturbance occurs, the system load continuously changes at a varying rate.
Consider the daily load cycle pattern shown in figure.
Generally the changes in load profile vary slowly, except during the mornings when the load change can be of the order of 100MW or more per minute (industries, offices and commercial places start business after 8am, which increases the loads at a high rate).

34. Example – Two Machine System - Line Removal After Fault
Effect of daily load cycle
Such rapid rise of load causes a significant change in system conditions.
The residual voltage error is corrected by slow-response methods (e.g. transformer tap change, switching of lines, capacitors, resistors, etc).
Rapid response compensators are not usually required for compensation during load changes.
However, if they are already installed (for other purposes such as transient stability improvement) they will definitely help maintain the voltage profile.