Power Electronics Assignment



For further information, please read Muhammad H. Rashid, Power Electronics, Chapter 13, Flexible Ac Transmission Systems.

This following information is trying to answer review questions 13.1 – 13.17 at the Muhammad H. Rashid, Power Electronics, Chapter 13, Flexible Ac Transmission Systems, page 599 with all of the paragraphs and figures taken from the book. No commercial purposes. It is written for fulfilling Power Electronics lecturer assignment.

1. What are the parameters for controlling power in transmission line? [Muhammad H. Rashid, Power Electronics, Chapter 13, Flexible Ac Transmission Systems, page 572 – 573 ]

Solution: Power and current flow can be controlled by one of the following means:

  1. Applying a voltage in the midpoint can also increase or decrease the magnitude of power.
  2. Applying a voltage in series with the line, and in phase quadrature with the current flow, can increase or decrease the magnitude of current flow. Because the current flow lags the voltage by 900, there is injection of reactive power in series.
  3. If a voltage with a variable magnitude and a phase is applied in series, then varying the amplitude and phase angle can control both the active and reactive current flows. This requires injection of both active power and reactive power in series.
  4. Increasing and decreasing the value if the reactance X cause a decrease and increase of the power height of the curves, respectively, as shown in Figure 13.1c. for given power flow, varying X correspondingly varies the angle δ between the terminal voltages.
  5. Power flow can also be controlled by regulating the magnitude of sending and receiving end voltages Vs and Vr. This type of control has much more influence over the reactive power flow than the active power flow.


Therefore, we can conclude that the power flow in a transmission line can be controlled by (1) applying a shunt voltage Vm at the midpoint, (2) varying the reactance X, and (3) applying a voltage with a variable magnitude in series with line.

2. What is the basic principle of shunt compensation? [Muhammad H. Rashid, Power Electronics, Chapter 13, Flexible Ac Transmission Systems, page 573 ]

Solution: The ultimate objective of applying shunt compensation in a transmission system is to supply reactive power to increase the transmittable power and to make it more compatible with the prevailing load demand. Thus, the shunt compensator should be able to minimize the line overvoltage under light load conditions, and maintain voltage levels under heavy load conditions. An ideal shunt compensator is connected at the midpoint of the transmission line, as shown in Figure 13.2a.The compensator voltage that is in phase with the midpoint voltage Vm has amplitude of V identical to that of the sending- and receiving-end voltages. That is Vm = Vs = Vr = V. the midpoint compensator in effect segments the transmission line into two independent parts: (1) the first segment, with an impedance of jX/2, carries power  from sending-end to the midpoint, and (2) the second segment, also with an impedance of jX/2, carries power from the midpoint to the receiving end.


3.  What is a thyristor-controlled reactor (TCR)? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 575 – 576]

Solution: A thyristor-controlled reactor (TCR) consists of a fixed (usually air-cored) reactor of inductance L and a bidirectional thyristor switch SW, as shown in Figure 13.3 a.


The current through the reactor can be controlled from zero (when the switch is open) to maximum (when the switch is closed)  by varying the delay angle α of the thyristor firing. This is shown in Figure 13.3b where σ is the conduction angle of the thyristor switch such that σ = П – 2α. When α = 0, the switch is permanently closed and it has no effect of the inductor current. If the getting of the switch is delayed by angle α with respect to crest (or peak) Vm of the supply voltage. V(t) = Vm cosωt = √2 V cos ωt, the instantaneous inductor current can be expressed as a function of α as follows:

Capture3.1                                                                       (13.11)

Which is valid for α≤ ωt ≤ П – α. For the subsequent negative half-cycle interval, the sign of the terms in Eq. (13.11) becomes opposite. The term (Vm/ωL) sinα in Eq. (13.11) is simply an α dependent constant by which the sinusoidal current obtained at α=0 is offset, shifted down for positive, and up for negative half-current during half cycles. The current iL (t) is at maximum when α=0 and it is zero when α=П/2. The waveforms of iL(t) for various values of α(α1, α2, α3 α4,) are shown in Figure 13.3c.

4. What is a thyristor-switched capacitor (TSC)? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 577 – 578]

Solution: Thyristor-switched capacitor (TSC) consists of a fixed capacitance C, a bidirectional thyristor switch SW, and a relatively small surge-limiting reactor L. This is shown in Figure 13.4a. The switch is operated to turn either on or off the capacitor. Using KVL in Laplace’s domain of s, we get

Capture4.1                                                                                         (13.14)

where Vco is the initial capacitor voltage. Assuming sinusoidal voltage of v = Vm sin (ωt+α), Eq (13.14) can be solved for the instantaneous current i(t) as given by

Capture4.2 (13.15)

Where ωn is the natural frequency of the LC circuit as given by

                                                Capture4.3                                                           (13.16)

Capture4.4                                                                                            (13.17)


5. What are the rules for transient-free switching of thyristor-switched capacitor? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 578]

Solution: to obtain transient-free switching, the last two terms on the right-hand side of Eq. (13.15) must equal to zero, that is, the following conditions must be satisfied:

Condition 1

Capture5.1                                                                                             (13.18a)

Condition 2

Capture5.2                                                                                                                                (13.18b)

The first condition implies that the capacitor is gate at the supply voltage peak. The second condition means that the capacitor must be charged to a voltage higher than the supply prior to gating. Thus, for a transient-free operation, the steady-state current (when the TSC is closed) is given by

Capture5.3                                                            (13.19)

6. What is a static VAR compensator (SVC)? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 580]

Solution: A static VAR compensator (SVC) consist of TCRs in parallel with one or more TSCs [4,7]. The general arrangement of an SVC is shown in Figure 13.6. The reactive elements of the compensator are connected to the transmission line through a transformer to prevent the elements having to withstand full system voltage. A control system determines the exacts gating instants of reactors according to a predetermined strategy. The strategy usually aims to maintain the transmission line voltage at a fixed level. For this reason, the control system has a system voltage input taken through a potential transformer (PT); additionally, other input parameters (or variables) to the control system may exist. The control system ensures that the compensator voltage remains more or less constant by adjusting the condition angle [5,6].



7. What is a STATCOM? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 581]

Solution: An advance static VAR compensator is essentially a voltage-sourced converter, as shown in Figure 13.7. A current-source inverter can be also subtitud [11]. It is simply known as the statit compensator, STATCOM. If the line voltage V is in phase with the converter output voltage Vo and has the same magnitude so that Capture7.1, there can be no current following into or out the compensator and no exchange of reactive power with the line. If the converter voltage is now increased, the voltage difference between V and Vo  appears across the leakage reactance of the step-down transformer. As a result, a leading current with respect to V is drawn and the compensator behaves as a capacitor, generating VARs. Conversely, if V > Vo, then the compensator draws a lagging current, behaving as an inductor, and absorbs VARs. This compensator operates essentially like a synchronous compensator where the excitation may be greater or less than the terminal voltage. This operation allows continuous control using GTOs, MCTs, or IGBTs.


8. What is the basic principle of series compensation? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 582 – 583]

Solution: A voltage in series with the transmission line can be introduced to control the current flow and thereby the power transmission from the sending end to the receiving end. An ideal series compensator, represented by the voltage source Vc  is connected in the middle of a transmission line, as shown in Figure 13.8. The current flowing through the transmission line is given by:

Capture8.1                                                                                        (13.21)

If the series applied voltage Vc  is in quadrature with respect to the line current, the series compensator cannot supply or absorb active power. That is, the power at the source Vc  terminals can be only reactive. This means the capacitive or inductive equivalent impedence may be replace the voltage source Vc.


9. What is a thyristor-switched series capacitor (TSSC)? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 585 – 586]

Solution: A thyristor-switched series capacitor (TSSC) consists of a number of capacitors in series, each shunted by a switch composed of two antiparallel thyristors. The circuit arrangement is shown in Figure 13.10a. A capacitor is inserted by turning off, and it is bypassed by turning on the corresponding thyristor switch. Thus, if all switches are off, the equivalent capacitance of the string becomes Ceq = C/m and  if all switches are turned on simultaneously, Ceq = 0. The amount of effective capacitance and hence the degree of series compensation are controlled in a steplike manner by increasing or decreasing the number of series capacitors inserted.


10. What is a thyristor-controlled series capacitor (TCSC)? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 586]

Solution: the TCSC consist of the series-compensating capacitor shunted by a thyristor-controlled reactor (TCR), as shown in Figure 13.11. this arrangement is similar in structure to the TSSC. If the impedance of the reactor XL is sufficiently smaller than that of the capacitor Xc, it can be operated in an on-off manner like the TSSC. Varying the delay angle α can vary the inductive impedance of the TCR. Thus the TCSC can provide a continuously variable capacitor by means of partially cancelling the affective compensating capacitance by the TCR. Therefore, the steady state impedance of the TCSC is that of a paralled LC circuit, consisting of a fixed capacitive impedance XC and variable inductive impedance XL. The effective impedance of the TCSC is given by

Capture10.1                                                                                            (13.27a)


11. What is a forced-commutation-controlled series capacitor (FCSC)? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 587 – 588]

Solution: The forced-commutation-controlled series capacitor (FCSC) consist of a fixed capacitor in parallel with a forced-commutation type of device such as a GTO, an MCT, or an IGBT. A GTO circuit arrangement is shown in Figure 13.12a. it is similar to the TSC, except the bidirectional thyristor switch is replaced by a bidirectional forced commutated device. When the GTO switch SW is closed, the voltage across the capacitor vc is zero; when the switch is open, vc becomes a maximum. The switch can control the ac voltage vc across the capacitor at a given line current i. Therefore, by closing and opening of the switch in each half-cycle in synchronism with the ac system frequency can control the capacitor voltage.


12. What is a series static VAR compensator (SSVC)? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 589]

Solution: the use of TSC, TCSC, of FCSC would allow capacitive series compensation. A series static VAR compensator (SSVC) consists of one of the series compensators. The general arrangement of an SSVC is show in Figure 13.13 with a TCSC. The control system receives a system voltage input taken form a PT and a system current input taken from a current transformer (CT). there may be other additional input parameters to the control system. The control strategy of the series compensator is typically based on achieving an objective line power flow in addition to the capability of damping power oscillations.


13. What is a series STATCOM? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 589 – 590]

Solution: This series compensator is the dual circuit of the shunt version Figure 13.7. Figure 13.14 shows the general arrangement of an advanced series compensator. It uses the voltage-source inverter (VSI) with a capacitor in its dc converter to replace the switched capacitors of the conventional series compensators. The converter output is arrange to appear in series with the transmission line via the use of the series transformer. The converter output voltage VC, which can be set to any relative phase, and any magnitude within its operating limits, is adjusted to appear to lead the line current by 900, thus behaving as a capacitor. If the angle between Vc and the lien current was not 900, then this would imply that the series compensator exchanges active power with the transmission line, which is clearly impossible because the compensator in Figure 13.14 has no active power source.


                This type of series compensation can provide a continuous degree of series compensation by varying the magnitude of Vc. Also, it can reverse the phase of VC, thereby increasing the overall line reactance; this may be desirable to limit fault current, or to dampen power oscillations. In general, the controllable series compensator can be used to increase transient stability, to dampen subsynchronous resonance whereother fixed capacitors are used, and to increase line power capability.

14. What is the basic principle of phase-angle compensation? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 592]

Solution: Phase-angle compensation is a special case of the series compensator in Figure 13.8. The power follow is controlled by phase angle. The phase compensator is inserted between the sending-end generator and the transmission line. This compensator is an ac voltage source with controllable amplitude and phase angle. An ideal phase compensator is shown Figure 13.16a. The compensator controls the phase difference between the two ac systems and thereby can control the power exchanged between the two ac systems. The effective sending-end voltage Vs and the compensator voltage Vσ, as shown in the phasor diagram in Figure 13.16b. the angle σ between Vs and Vσ can be varied in such a way that the angle σchange does not result in magnitude change. That is,

Capture14.1                                                                                                (13.31a)

Capture16.1                                                            (13.31b)

By controlling the angle σ independently, it is possible to keep the transmitted power at the desired level, independent of the transmission angle δ.


15. What is a phase shifter? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 595]

Solution: The phase shifter controls the magnitude of Vq and thus the phase shift α to the sending-end voltage [8]. This control can be achieved either by sensing the generator angle, or from using power measurements. The controller can also be set to dampen power oscillations. Phase shifters like series capacitor compensators allow control of power through the network and power sharing between parallel circuits. Series capacitors are more suitable for long-distance lines because unlike phase shifters, they effectively reduce line reactance and hence the reactive power and voltage control problem associated with long-distance transmission. Phase shifters are more suitable for power flow control in compact high power density networks.

16. What is a quadrature booster (QB)? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 593 – 594]

Solution: If angle σ of phasor Vσ relative to phasor VS is mainted fixed at ± 900, the phase compensator becomes a quadrature booster (QB) that has the following relationship:

Capture16.1                                                                                                (13.37a)

Capture16.2                                                                     (13.37b)

The phasor diagram of the QB-type angle compensator is shown in Figure 13.17a and its transmitted power Pb with the booster compensator is given by

Capture16.3                                                                            (13.38)

The transmitted power Pb versus angle δ as a parametric function of the applied quadrature voltage Vσ is shown in Figure 13.17b. the maximum transmittable power increases with the applied voltage Vσ, because in contrast to the phase-angle compensator. The QB increases the magnitude of the affective sending-end voltage.


17. What is a unified power flow controller (UPFC)? [Muhammad H. Rashid, Power Electronics,Chapter 13, Flexible Ac Transmission Systems, page 596]

Solution: A unified power flow controller (UPFC) consists of an advance shunt and series compensator with a common DC link, as shown in Figure 13.19a. The energy-sorting capacity of the dc capacitor is generally small. Therefore, the active power drawn (generated) by the shunt converter should be equal to the active power generated (drawn) by the series converter. Otherwise, the dc-link voltage may increase or decrease with respect to the rated voltage, depending on the net power in the shunt or series converter can be shown independently, giving a greater flexibility to the power flow control [9].


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