# Facts Theory

## Chapter 1:- FACTS Concepts and general system consideration

**Q.1) State the importance of use of FACTS devices in power transmission.**

**Give suitable example.**

**Answer:-**

- The FACTS Controllers has the ability to control the interrelated parameters that govern the operation of transmission systems including series impedance, shunt impedance, current, voltage, phase angle, and the damping of oscillations at various frequencies below the rated frequency.
- These constraints cannot be overcome, while maintaining the required system reliability, by mechanical means without lowering the useable transmission capacity. Whereas FACTS Controllers can enable a line to carry power closer to its thermal rating.
- FACTS technology opens up new opportunities for controlling power and enhancing the usable capacity of present, as well as new and upgraded, lines.
- The possibility that current through a line can be controlled at a reasonable cost.
- Boost the voltage of existing lines.
- Enable corresponding power to flow through such lines under normal and contingency conditions.
- Enabling utilities to get the most service from their transmission facilities and enhance grid reliability.
- The FACTS technology is not a single high-power Controller, but rather a collection of controllers, which can be applied individually or in coordination with others to control one or more of the interrelated system parameters.

**Q.2) What is loading capability of transmission line ?**

**Explain in the limits of loading capacity of transmission line.**

**Answer:-**

- Thermal
- Dielectric
- Stability

**Thermal:-**

**Dielectric:-**

**Stability:-**

- Transient stability
- Dynamic stability
- Steady-state stability
- Frequency collapse
- Voltage collapse
- Subsynchronous resonance

**Q.3) From first principle derive power flow equation, 𝑷 =**

__E1E2__𝒔𝒊𝒏𝜹

**Q.4) How FACTS controllers are classified? Explain in brief.**

**OR**

**Q.4) What is FACTS controller? Clarify distinguish between FACTS controllers with each other.**

**Answer:-**

**FACTS Controller:-**

- Series Controllers
- Shunt Controllers
- Combined series-series Controllers
- Combined series-shunt Controllers

**Combined series-series Controllers: [Figure (d)]**

## CHAPTER 3: STATIC SHUNT COMPENSATOR

**Q.1) Explain with neat vector diagram, how transient stability improves with ideal midpoint compensators.**

**OR**

**Q.1) Explain how stability margin is increased when shunt compensator is used for transmission line.**

**Answer:-**

**How stability margin improves?**

**Q.2) Explain effect of use of shunt compensators on receiving end voltage stability.**

**Answer:-**

**Q.3) State the requirements of good shunt compensators.**

**Answer:-**

- The compensator must stay in synchronous operation with the ac system at the compensated bus under all operating conditions including major disturbances. Should the bus voltage be lost temporarily due to nearby faults, the compensator must be able to recapture synchronism immediately at fault clearing.
- The compensator must be able to regulate the bus voltage for voltage support and improved transient stability, or control it for power oscillation damping and transient stability enhancement, on a priority basis as system conditions may require.
- For a transmission line connecting two systems, the best location for VAr compensation is in the middle, whereas for a radial feed to a load the best location is at the load end.

**Q.4) Explain the working principle of TSC in shunt compensation.**

**OR**

**Q.4) Differentiate between TCR and TSC compensators based on working conditions, operating V-I area, harmonics/ transients. Also draw neat diagram of TSC and TCR.**

**TCR**

**A. Working conditions:-**

**TCR**

**B. Operating V-I area:-**

**C. Harmonics/ Transients:-**

**TSC**

**A. Working conditions:-**

**B. Operating V-I area:-**

**C. HARMONIC/TRANSIENTS:**

**Q.5) Draw and explain losses versus VAr-output characteristics of FC-TCR.**

**Answer:-**

**Q.6) Explain switching converter type VAr generators with basic operating principle and control approach.**

**OR**

**Q.6) Explain working of 3 ph-12 pulse converter used for generation of reactive power.**

**Answer:-**

**Operating principle:-**

**Figure:- Reactive power generation by rotating a voltage-sourced switching converter.**

## Chapter 4 :- Static Series Compensators

**Q.1) With a neat schematic diagram, explain series capacitive compensation (SCC).**

** OR **

**Q.1) What is series compensation? How it is obtained in transmission line.**

**Answer:- **

The reactive shunt compensation is highly effective in maintaining the desired voltage profile along the transmission line interconnecting two busses of the ac system and providing support to the end voltage of radial lines in the face of increasing power demand. Thus, reactive shunt compensation, when applied at sufficiently close intervals along the line, could theoretically make it possible to transmit power up to thermal limit of the line, if a large enough angle between the two end voltages could be established. However, shunt compensation is ineffective in controlling the actual transmitted power which, at a defined transmission voltage, is ultimately determined by the series line impedance and the angle between the end voltages of line.

Controllable series line compensation is a cornerstone of FACTS technology. It can be applied to achieve full utilization of transmission assets by controlling the power flow in the lines, preventing loop flows and, with the use of fast controls, minimizing the effect of system disturbances, thereby reducing traditional stability margin requirements. The effect of series compensation on the basic factors, determining maximal power transmission, steady- state power transmission limit, transient stability, voltage stability and power oscillation damping, will be examined.

The basic idea behind series capacitive compensation is to decrease the overall effective series transmission impedance from the sending end to the receiving end, i.e., X in the P = (V2 / X) sinδ relationship characterizing the power transmission over a single line.

Consider the simple two-machine model, analogous to that shown for shunt compensation in Figure, but with a series capacitor compensated line, which, for convenience, is assumed to be composed of two identical segments, as illustrated in Figure (a). The corresponding voltage and current phasors are shown in Figure (b). Note that for the same end voltages the magnitude of the total voltage across the series line inductance, Vx = 2Vx/2 is increased by the magnitude of the opposite voltage, Vc , developed across the series capacitor; this results from an increase in the line current. The effective transmission impedance Xeff with the series capacitive compensation is given by

Assuming Vs = Vr = V in Figure (b), the current in the compensated line, and the corresponding real power transmitted, can be derived in the following forms

The relationship between the real power P, series capacitor reactive power Qc, and angle δ is shown plotted at various values of the degree of series compensation k in Figure (c). It can be observed that, as expected, the transmittable power rapidly increases with the degree of series compensation k. Similarly, the reactive power supplied by the series capacitor also increases sharply with k and varies with angle δ in a similar manner as the line reactive power.

In order to increase the current in the given series impedance of the actual physical line (and thereby the corresponding transmitted power), the voltage across this impedance must be increased. This can be accomplished by an appropriate series connected circuit element, such as a capacitor, the impedance of which produces a voltage opposite to the prevailing voltage across the series line reactance and, as the phasor diagram in Figure (c) illustrates, thereby causes this latter voltage to increase. Thus, an alternate compensating circuit element may be envisioned as an ac voltage source which directly injects the desired compensating voltage in series with the line.

**Q.2) Explain improvement of transient stability using series compensation.**

**Answer:-**

Transient stability improvement by controlled shunt compensation is achieved by increasing the power transmission via increasing (or maintaining) the (midpoint) transmission line voltage during the accelerating swing of the disturbed machine(s). The powerful capability of series line compensation to control the transmitted power can be utilized much more effectively to increase the transient stability limit and to provide power oscillation damping.

Consider the simple system with the series compensated line shown in Figure. it is, for convenience, also assumed for the series compensated case that the pre-fault and post-fault systems remain the same.

Suppose that the system of Figure above, with and without series capacitive compensation, transmits the same power Pm. Assume that both the uncompensated and the series compensated systems are subjected to the same fault for the same period of time.

The dynamic behavior of these systems is illustrated in Figures (a) and (b). As seen, prior to the fault both of them transmit power Pm at angles δt and δst , respectively. During the fault, the transmitted electric power becomes zero while the mechanical input power to the generators remains constant, Pm. Therefore, the sending-end generator accelerates from the steady-state angles δt and δst to angles δ2 and δs2, respectively, when the fault clears. The accelerating energies are represented by areas A1 and Ast • After fault clearing, the transmitted electric power exceeds the mechanical input power and therefore the sending-end machine decelerates. However, the accumulated kinetic energy further increases until a balance between the accelerating and decelerating energies, represented by areas A1, Ast , and A2, As2, respectively, is reached at the maximum angular swings, δ3 and δs3 , respectively. The areas between the P versus δ curve and the constant Pm; line over the intervals defined by angles δ3 and δcrit and δs3 and δcrit respectively, determine the margin of transient stability, represented by areas Amargin and Asmargin.

Comparison of Figures (a) and (b) clearly shows a substantial increase in the transient stability margin the series capacitive compensation can provide by partial cancellation of the series impedance of the transmission line. The increase of transient stability margin is proportional to the degree of series compensation. Theoretically this increase becomes unlimited for an ideal reactive line as the compensation approaches 100%. However, practical series capacitive compensation does not usually exceed 75% for a number of reasons, including load balancing with parallel paths, high fault current, and the possible difficulties of power flow control. From the standpoint of transient stability, and of overall system security, the post-fault system is the one that matters. That is, power systems are normally designed to be transiently stable, with defined pre-fault contingency scenarios and post-fault system degradation, when subjected to a major disturbance. For this reason, in most practical systems, the actual capacity of transmission networks is considerably higher than that at which they are normally used. The powerful capability of series compensation, with sufficiently fast controls, to handle dynamic disturbances and increase the transmission capability of post fault or otherwise degraded systems, can be effectively used to reduce the "by-design" underutilization of many power systems.

**Q.3) Explain the working of TSSC with neat diagram. **

**Answer:- **

The basic circuit arrangement of the thyristor-switched series capacitor is shown in Figure 6.10. It consists of a number of capacitors, each shunted by an appropriately rated bypass valve composed of a string of reverse parallel connected thyristors, in series. As seen, it is similar to the circuit structure of the sequentially operated GCSC shown in Figure 6.9, but its operation is different due to the imposed switching restrictions of the conventional thyristor valve.

The operating principle of the TSSC is straightforward: the degree of series compensation is controlled in a step-like manner by increasing or decreasing the number of series capacitors inserted. A capacitor is inserted by turning off, and it is bypassed by turning on the corresponding thyristor valve. A thyristor valve commutates "naturally," that is, it turns off when the current crosses zero. Thus a capacitor can be inserted into the line by the thyristor valve only at the zero crossings of the line current. Since the insertion takes place at line current zero, a full half-cycle of the line current will charge the capacitor from zero to maximum and the successive, opposite polarity half-cycle of the line current will discharge it from this maximum to zero, as illustrated in Figure 6.11. As can be seen, the capacitor insertion at line current zero, necessitated by the switching limitation of the thyristor valve, results in a de offset voltage which is equal to the amplitude of the ac capacitor voltage. In order to minimize the initial surge current in the valve, and the corresponding circuit transient, the thyristor valve should be turned on for bypass only when the capacitor voltage is zero. With the prevailing de offset, this requirement can cause a delay of up to one full cycle, which would set the theoretical limit for the attainable response time of the TSSC.

The TSSC can control the degree of series compensation by either inserting or bypassing series capacitors but it cannot change the natural characteristic of the classical series capacitor compensated line. This means that a sufficiently high degree of TSSC compensation could cause subsynchronous resonance just as well as an ordinary capacitor. In principle, the TSSC switching could be modulated to counteract subsynchronous oscillations. However, considering the relatively long switching delays encountered, the modulation is likely to be ineffective, if not counterproductive, except for the very low end of the subsynchronous frequency band. Therefore, the pure TSSC scheme of Figure 6.10 would not be used in critical applications where a high degree of compensation is required and the danger of subsynchronous resonance is present Nevertheless, the TSSC could be applied for power flow control and for damping power oscillation where the required speed of response is moderate.

The basic V-I characteristic of the TSSC with four series connected compensator modules operated to control the compensating voltage is shown in Figure 6.12(a1). For this compensating mode the reactance of the capacitor banks is chosen so as to produce, on the average, the rated compensating voltage, VCmax = 4Xc I min, in the face of decreasing line current over a defined interval I min sIs I max• As the current I min is increased toward I max, the capacitor banks are progressively bypassed by the related thyristor valves to reduce the overall capacitive reactance in a step-like manner and thereby maintain the compensating voltage with increasing line current. In the impedance compensation mode, the TSSC is applied to maintain the maximum rated compensating reactance at any line current up to the rated maximum, as illustrated in Figure 6.12(bl).

In this compensation mode the capacitive impedance is chosen so as to provide the maximum series compensation at rated current, 4Xc = Vcmax/Imax, that the TSSC can vary in a step-like manner by bypassing one or more capacitor banks. The loss versus line current characteristic for this compensation mode is shown in Figure 6.12(b2) for zero compensating impedance .The TSSC may also have transient ratings, usually defined as a function of time. Outside the defined ratings the TSSC would be protected against excessive current and voltage surges either by external protection across the capacitor and the parallel valve or, with sufficient rating, by the valve itself in bypass operation.

**Q.6) Draw a block diagram and explain internal control scheme for SSSC employing indirectly controlled converter. **

**Answer:- **

The voltage-sourced converter-based series compensator, called Static Synchronous Series Compensator (SSSC), was proposed by Gyugyi in 1989 within the concept of using converter-based technology uniformly for shunt and series compensation, as well as for transmission angle control.

The basic operating principles of the SSSC can be explained with reference to the conventional series capacitive compensation of Figure, shown simplified in Figure together with the related voltage phasor diagram. The phasor diagram clearly shows that at a given line current the voltage across the series capacitor forces the opposite polarity voltage across the series line reactance to increase by the magnitude of the capacitor voltage.

Thus, the series capacitive compensation works by increasing the voltage across the impedance of the given physical line, which in turn increases the corresponding line current and the transmitted power. While it may be convenient to consider series capacitive compensation as a means of reducing the line impedance, in reality, as explained previously, it is really a means of increasing the voltage across the given impedance of the physical line. It follows therefore that the same steady-state power transmission can be established if the series compensation is provided by a synchronous ac voltage source, as shown in Figure , whose output precisely matches the voltage of the series capacitor, i.e.,

For normal capacitive compensation, the output voltage lags the line current by 90 degrees. For SVS, the output voltage can be reversed by simple control action to make it lead or lag the line current by 90 degrees. In this case, the injected voltage decreases the voltage across the inductive line impedance and thus the series compensation has the same effect as if the reactive line impedance was increased. With the above observations, a generalized expression for the injected voltage, Vq can simply be written:

## Chapter 5:- Static voltage and phase angle regulator

### A. Objectives of voltage and phase angle regulator:

**1. Thyristor controlled voltage regulator (TCVR):**

- In a voltage regulator, the voltage regulator is obtained by injecting voltage in phase with the system voltage.
- In thyristor controller voltage regulator (TCVR) the thyristor switches are used to control the injected voltage.
- In TCVR, the transformer winding is so connected such that the injected voltage should be in the same phase with the system voltage.
- By controlling the value of the delay angle of thyristor required voltage regulation can be obtained.
- The circuit diagram of TCVR is same as thyristor controlled tap changer and is shown in Fig. (1).

**2. Thyristor controlled phase angle regulator (TCPAR):**

- In the phase angle regulator, the phase angle regulation is obtained by injecting voltage in phase quadrature with the system voltage.
- In thyristor controlled phase angle regulator (TCPAR) the thyristor switches are used to control the injected voltage.
- In TCPAR the transformer winding is so connected such that the injected voltage should be in phase quadrature with the system voltage.
- By controlling the value of the delay angle of thyristor required phase angle regulation can be obtained.

**Thyristor tap changer with resistive load:**

- In the above circuit, the complete secondary winding of the transformer is split into two part.
- The lower terminal and the midpoint winding is operated by switch SW1.
- When switch SW1 is closed the voltage across the resistive load is V1.
- The complete secondary winding will be connected across load R when the switch SW2 is closed and the voltage across the load is V2
- The gate of thyristor valves SW1 and SW 2 is controlled by the delay angle α with respect to the zero crossing instant of the voltage.
- The waveform of the voltages with respect to delay angle a is as shown in Fig. (2)

- From the waveform at α = 0, thyristor switch SW turns on and a voltage across the load is v1.
- At α, valve SW2 is turned ON which commutates the current from the conducting thyristor valve SW1, by forcing a negative anode to cathode voltage across it and connecting the output to the upper tap with voltage V2.
- Valve SW2 continues conducting until the next current zero is reached, whereas the previous gating sequence continues as shown by the load voltage waveform.
- Fourier analysis of the output voltage waveform for continuously controlled thyristor tap changer, operating between V1 and V2 which resistive load can be given by the equation:

- By using the above equation the resultant regulated voltage of tap changer can be obtained.

### B. Switching converter based voltage and phase angle regulator:

_{c}e

^{+/-jψ.}

^{}

^{}

## Chapter 6:- Unified Power Flow Controller (UPFC)

The Unified Power Flow Controller (UPFC) concept was proposed by Gyugyi in 1991. The UPFC was devised for the real-time control and dynamic compensation of ac transmission systems, providing multifunctional flexibility required to solve many of the problems facing the power delivery industry. The UPFC is able to control, simultaneously or selectively, all the parameters affecting power flow in the transmission line (i.e., voltage, impedance, and phase angle), and this unique capability is signified by the adjective "unified" in its name. Alternatively, it can independently control both the real and .reactive power flow in the line.

### A. Basic Operating Principle:

The UPFC is the most versatile FACTS controller developed so far, with all encompassing capabilities of voltage regulation, series compensation, and phase shifting.

1. It can independently and very rapidly control both real- and reactive power flows in a transmission.

2. It is configured as shown in Fig. and comprises two VSCs coupled through a common dc terminal.

The implementation of the UPFC using two “back – to –back” VSCs with a common DCterminal capacitor

3. One VSC converter 1 is connected in shunt with the line through a coupling transformer; the other VSC converter 2 is inserted in series with the transmission line through an interface transformer.

4. The dc voltage for both converters is provided by a common capacitor bank.The series converter is controlled to inject a voltage phasor Vpq, in series with the line, which can be varied from 0 to Vpq max. Moreover, the phase angle of Vpq can be independently varied from 00 to 3600

5. In this process, the series converter exchanges both real and reactive power with the transmission line.

6. Although the reactive power is internally generated/ absorbed by the series converter, the real-power generation/ absorption is made feasible by the dc-energy–storage device that is, the capacitor.

7. The shunt-connected converter 1 is used mainly to supply the real-power demand of converter 2, which it derives from the transmission line itself. The shunt converter maintains constant voltage of the dc bus.

8. Thus the net real power drawn from the ac system is equal to the losses of the two converters and their coupling transformers.

In addition, the shunt converter functions like a STATCOM and independently regulates the terminal voltage of the interconnected bus by generating/ absorbing a requisite amount of reactive power.