1. by Debashish Mishra Regd.No:0701227276 1 A Current Regulated Switched Capacitor Static Volt Ampere Reactive Compensator

2. Background The SVC with switch capacitor 1)Inductive Mode 2)Capacitive Mode The power flow inside the SVC Flow of power when line current contains useful harmonics Conclusion Reference 2

3. The significance of power factor (PF) correction is reflected in the large number of documents addressing this subject, in the engineering design effort, and in the numerous industrial plants that manufacture equipment for the control of reactive power and filtering of current harmonics [l]. Some of the benefits derived from correct PF adjustment are: 1. reduced energy loss; 2. released generation, transmission, distribution, and substation capacity. 3. reduced voltage drop and improved voltage regulation.etc 3

4. Traditionally, fixed linear capacitors are used at almost voltage level to achieve the desired kVAr.Some capacitors are installed as switched-capacitor banks to maintain a “horizontal” voltage profile along the feeders or to avoid over- compensation. Disadvantages:- *Coarse incremental chages *Undesirable transient s generated during the switching and the possibility of obtaining resonant or near resonant topologies at harmonic frequencies. The first practical device performing as a variable capacitance or inductance was the “synchronous condenser”. It has two major limitations 1.slow response 2.special maintenance requirement 4

5. To overcome these disadvantages thystorized static var compensator(SVC) was developed. The basic component of svc is a bidirectional switch T with an inductance. T he working of the circuit can be understood if we replace the switch T with an equivalent voltage. The fundamental component of the fictitious voltage is a function of conduction angle 5

6. By varying the conduction angle it is possible to control the reactive power delivered by the voltage source in the same manner as the emf magnitude E controls the flow of Q. The voltage has two components, the fundamental and the voltage comprising all of the harmonics. The active power supplied by the purely sinusoidal source is partly dissipated in the feeder resistor R and the rest is delivered to the fictitious voltage source. Assuming the switch T to be lossless results 6

7. This means that the 60 Hz active power P, supplied to the switch is all converted in harmonic active power PH. where and 7

8. The topology of the circuit is presented in the fig. below The line current “i” is allowed to zigzag within the upper and lower boundaries of a desired current template 8

9. T he coil voltage determines the slope of the current. T he switching sequence of the four switches and helps control the polarity of A t any moment the capacitor voltage D uring the positive half –cycle, the switch is closed and is opened. When the switch is closed and is opened and this causes When open and closed causing D uring negative-half cycle, is closed and is open. In this case is closed and is opened. Thus and Closing and opening causes and I t results from here that is closed and is opened from the lower boundary to the upper boundary irrespective of the polarity of the ac voltage ; and is opened and is closed during the current transition from the upper boundary to the lower boundary. 9

10. 10 If the error band is made smaller, the switching frequency will increase and at the same time the current waveform will become more smooth. The capacitor voltage at the beginning of each half-cycle is equal Since this system is lossless and the net electric energy transferred from the source to the SVC is nil there is no change in the net level of the electric charge stored in the capacitor C. For each switching cycle “k” the average value of the switched voltage, is controlled by the duty cycle and the average value of the capacitor voltage -----------------(1) If the voltage source ----------------------(2) And the line current is --------------------(3) The fundamental voltage used to control the flow of the kVar is --------------(4)

11. 11 For the kth switching interval, assuming becomes ---------------(5) At any moment the energy generated by the source U is stored in the fields of L and C. Therefore, the balance of power implies that ----------------(6) Substituting (2) and (3) in (6) gives --------------(7) Where is the magnitude of the reactive power. The rearrangement of term in (7) yeilds Integration of the above equation results in

12. 12 where K is the integration constant. At t = 0, results ----------(8) The magnitude of the reactive power flowing from to SVC is ---------------(9) The expression for the normalized reactive power is ---------(10) The normalized capacitor initial voltage ------(11) The resonance frequency -------(12) Substituting (10),(11),(12) in (8) gives -------(13)

13. 13 Where -----------------(14) In practical application and this makes 2m<0.5 can be approximated as ------------------(15) Where ---------------(16) And ------------(17) Substituting (8) in (5), the value of the duty cycle for the kth switching interval is ------------------(18) where ------------(19)

14. 14 The modulation of the duty cycle, and hence the control of the reactive power, is a function of, and. And the normalized reactive power is -------------------(20) There are to modes of operation to obtain the result 1.Inductive mode 2.capacitive mode INDUCTIVE MODE For inductive mode of the SVC operation, the maximum value of the duty cycle occurs for and --------------(21) Therefore -------------(22) Substituting (14),(17) and (22) into (20) -------------(23)

15. 15 Therefore --------------(24) CAPACITIVEMODE In practical range of operation of the SVC,2m<0.5. For this situation a<1/3 and maximum value of the duty cycle for the capacitive mode is attained when.This implies --------(25) For,which is beyond the practical range, maximum value of the duty cycle is obtained for which yields --------(26) Substituting (14), (17), and (25) into (20) gives ------------(27)

16. 16 Therefore,

17. 17 This analysis is implemented by using the method developed in the fig. below The four switches and are replaced with the voltage sources and. The waveform of the voltage and is given by

18. 18 And Where And The voltage spectra of for is presented as

19. 19 [Harmonic spectra of the voltage normalized w.r.t. ]

20. 20 The equivalent circuit of the SVC with switched capacitor is represented as

21. 21 The voltage impressed across the bridge terminal is And the voltage across the capacitor is The spectrum of contains only very high harmonics and for all practical purposes the effect of on the line current can be neglected. The bridge acts like a variable capacitor or inductor and the reactive power flows from the source to the bridge and the inductance L. Ignoring,the oscillation of power between the source and the bridge is -----(28) The energy stored in the capacitor is -------(29)

22. 22 Substitution of (13) in (29) gives And the capacitor power is -------(30) Substituting (10), (11), (12), and (14) into (30) yields --------(31) The equality of two instantaneous powers given by (28) and (31) proves that the same oscillation of energy is exhibited at the bridge terminals and the capacitor terminals.

23. 23 This is the operation of the circuit as an active filter. It requires that the line current contains lower order harmonics besides the fundamental. For example, Assuming the line current to contain a harmonic of harmonic order ‘h’ i.e., ------(32) The flow of fundamental and harmonic reactive power is controlled with the switched voltage For the capacitor voltage, substitution of (32) and (2) in (6) gives

24. 24 -------(33) Comparison of (33) with (13) reveals that the dc component of stands modified owing to the presence of additional terms. The capacitor voltage also contains oscillation of and frequencies.

25. The concept presented in the above is understanding the mechanism of energy flow in any type of static converter. It provides insight into the process of flow power frequency reactive power as well as harmonic frequency reactive power. The SVC circuit presented in this topic is analyzed by replacing the four bidirectional switches with equivalent non-sinusoidal voltages Each non-sinusoidal voltage sources of different frequencies. The power flow is controlled by adjusting the magnitude and phase angles of the fictitious voltages. This is done by pulse- width modulation of the switches. The circuit presented can perform in three distinctive ways depending on the desired line current waveform and the type of output load; 25

26. 1) SVC operation with sinusoidal current waveform. In this case the line current is nearly sinusoidal and in quadrature with the voltage. 2) SVC operation with non-sinusoidal current waveform. The converter in this mode of operation can called an active filter. The voltage drop across the switches must “cause the generation” of the desired, useful current harmonics in this case as opposed to a sinusoidal line current in the previous case. 3) The active power line conditioner operation. Active power is transferred to/from the output load. the experimental result obtained from a laboratory prototype and the mathematical model developed to the study of the energy losses and the limitations of the new concept will be presented in the subsequent topic. 26

27. 27

28. [l] M. Zucker and J. J. Erhart, “Capacitors near loads? The engineering viewpoint,” IEEE Trans. Ind. Appl., vol. IA-21, no. 2, pp. 308-317, March/April, 1985. [2] R. H. Hopkinson, “Economic power factor, key to kVar supply,” Electrical Forum, vol. 6, no. 3, pp. 20-22, 1980. [3] J. J. Grainger and S. H. Lee, “Optimum size and location of shunt capacitors for reduction of losses in distribution feeders,” IEEE Trans. PAS, vol. 100, pp. 1105-1 118, March 1981 [4] F. G. Baum, “Voltage regulation and insulation for large power long distance transmission systems,” J. AIEE, no. 40, pp. 1017-1032, 1924. [5] T. J. E. Miller, Reactiile Power Control in Elecrric Systems. New York Wiley, 1982, Chapter, 6, 241. 28