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TCI) Static Var Compensator (SVC EJERS, European Journal of Engineering Research and Science Vol. 5, No. 12, December 2020 An R-L Static Var Compensator (SVC) A. J. Onah, E. E. Ezema and I. D. Egwuatu i i i i i Abstract — Traditional static var compensators (SVCs) L S L S L iS employ shunt reactors and capacitors. These standard reactive i Com i i i com power shunt elements are controlled to produce rapid and C L variable reactive power. Power electronic devices like the L S S thyristor etc. are used to switch them in or out of the network 1 2 Load(Z) Vm sint Vmsint C Load(Z) Vmsint Load(Z) S1 S2 to which they are connected in response to system conditions. S1 S2 There are two basic types, namely the thyristor-controlled R reactor (TCR), and the thyristor-switched capacitor (TSC). In C L this paper we wish to investigate a compensator where the reactor or capacitor is replaced by a series connected resistor TCR TSC TSRL and reactor (R-L). The performance equations are derived and applied to produce the compensator characteristics for each of the configurations. Their performances are compared, and the contrasts between them displayed. All three configurations are made to achieve unity power factor in a system. Index Terms — reactive power, static var compensator, resistor, inductor, power transmission. I. INTRODUCTION1 TCR TSC TSRL SVC is a shunt reactive compensation controller [1] Fig. 1. TCR, TSC and TSRL topologies. comprising of a combination of fixed capacitor or thyristor- switched capacitor in conjunction with thyristor-controlled reactor. SVCs have thus been used for years by utilities to II. THE TCR CONFIGURATION control reactive power flow in transmission and distribution Fig. 2 is the TCR configuration. systems and consequently, help to improve power factor, iL iS stabilize weak systems, minimize line I 2 R losses, increase i power transfer capability, enhance transient and steady-state iC stability, balance three-phase loads, damp oscillations, L reduce voltage flicker and provide greater dynamic voltage regulation [2]-[6]. Limiting the flow of load reactive current V sin t Load (Z) along the transmission lines reduces transmission losses m C S S which will, in turn, lead to substantial reduction in the cost 1 2 of both power capacity and energy production [7]. In principle, all shunt controllers inject current into the system at the point of connection [8]. The aim of this paper is to investigate a shunt static var compensator (SVC) which Fig. 2. Thyristor-Controlled Reactor (TCR). consists of series R-L elements in the place of the commonly used reactor or capacitor as reactive power In this SVC, a bank of static switches connected in anti- elements. The performance of this compensator is analyzed parallel is connected in series with an inductor [9]-[11]. and compared with the existing Thyristor-Controlled This arrangement is placed in parallel with one or more Reactor (TCR) and Thyristor-Switched Capacitor (TSC) constantly energized capacitor banks. This is also known as compensators. The proposed compensator is connected in fixed capacitor, thyristor-controlled reactor (FC-TCR) static parallel with and near the load. It provides dynamic var var compensator (SVC). A constant quantity of vars are compensation and uses combinations of resistive and supplied by the capacitor to the system, while the reactor inductive elements with solid-state devices, for switching to supplies variable lagging current in accordance with the achieve the goals stated above. The contrasts between this firing angle of the high-power switches. The inductive compensator configuration and the TCR and TSC are current counters the capacitive current. The firing angle is obtained and displayed. The three topologies are shown in varied between 90 and 180°, thereby adjusting continuously Fig. 1. the magnitude of current and apparent inductance of the reactor. Phase-angle (α) control gives rise to harmonic 1 Published on December 14, 2020. currents generation, and so filters are needed in order to A. J. Onah, Michael Okpara University of Agriclture, Umudike, Nigeria. produce harmonic-free current. E. E. Ezema, Enugu State Polytechnic, Iwollo, Nigeria. I. D. Egwuatu, Wiez Engineering, Nigeria. DOI: http://dx.doi.org/10.24018/ejers.2020.5.12.2253 Vol 5 | Issue 12 | December 2020 46 EJERS, European Journal of Engineering Research and Science Vol. 5, No. 12, December 2020 23−− It can be shown that the network in Fig. 2 is operating at V b= cos − cost sin ntdt − cos + cost sin ntdt n ( ) ( ) 2L + 0.7 power factor, where vSm= Vsin t and the load, Z=6+j6.1. Fig. 3 shows the source voltage ( v ), load (8) S The inductor current is shown in Fig. 4. current ( iL ) and load reactive power ( qL ).The rms values 2 of and is 220V and 25.7A respectively. The IR loss i of this system is equal to 793 W, where the line resistance R=1.2 Ω. i1 q L vS iL t Fig. 4. Inductor current. i Inductor current; i1 fundamental component. The total harmonic distortion (THD) of i is 24.3%. t The capacitor current is: Fig. 3 Source voltage, load current, and load reactive power. I= CV (9) The inductor current in Fig. 2 can be found as follows: Cm For the positive half-cycle of the system voltage: Thus, the compensator output current is: di L= Vm sin t (1) i=+ i I (10) dt com C The solution of equation (1) is a general solution given 2 as: The currents waveforms of the compensator are shown in V Fig. 5. i= −cos t + A (2) L i icom i where A is the constant of integration. 1 V At t = , i = 0 , and A = m cos . L So, V it=−(cos cos ) (3) L t Similarly, it can be shown that, for the negative half- Fig. 5. Currents’ waveforms of compensator. cycle, when t =+ . The compensator output current combines with the load V current to produce the resultant line current ( i ) from the it=+(cos cos ) (4) S L source, i.e. By Fourier analysis, the inductor (reactor) current is: iS=+ i L i com (11) 1 These currents are shown in Fig. 6. i= ao +() acosntbsinnt n + n (5) 2 n =1 23−− V ao =( cos − costdt ) −( cos + costdt ) 2L + (6) 23−− V an =( cos − cost ) cos ntdt −( cos + cost ) cos ntdt 2L + (7) DOI: http://dx.doi.org/10.24018/ejers.2020.5.12.2253 Vol 5 | Issue 12 | December 2020 47 EJERS, European Journal of Engineering Research and Science Vol. 5, No. 12, December 2020 III. THE TSC CONFIGURATION i L Fig. 9 shows the TSC configuration. i com iS iL iS iCom L Vm sin t Load (Z) S1 S 2 t Fig. 6. Load current, compensator current and line current. C The line current, together with the system voltage is shown in Fig. 7. Fig. 9. Thyristor-switched capacitor (TSC). vS TSC is a shunt-connected thyristor-switched capacitor whose effective reactance is varied in a stepwise manner by full- or zero-conduction operation of the switch [12]- i [13].The TSC configuration - Fig. 9 [14]-[15] consists of a S shunt capacitor bank which is switched on and off by a pair of anti-parallel switches. A small series damping inductor is used to limit the rate of rise of current through the switches and to prevent resonance with the system network. The capacitor current reaches a natural zero current when the voltage across the capacitor equals the maximum ac system Fig.7 System voltage and line current after compensation. voltage Vm. At this point, the gate pulses of the switches are suppressed, and reactive power through the capacitor ceases The system operating power factor has been raised to 1.0 abruptly. Harmonic currents generation by this SVC is quite by the application of the TCR, where α = 110o. The I 2 R low because of the zero-current switching [16]. When the loss of the transmission line is 468W – reduction of power switches are not conducting, the dc voltage on the capacitor loss by 41%. A filter will be required to suppress the and the ac system voltage add up to create voltage stresses harmonics. Fig. 8 shows the reactive powers due to the load of twice the system voltage across the switches. One of the and the compensator. main properties of this configuration is stepwise control. So, it has the disadvantage of non-continuous VAr compensation. The final information is the number of qcom capacitor banks to be connected to the ac system. The qL control must be rigidly synchronized to the ac system voltage, to avoid misfiring. Thus, it has complex control qS system. Each capacitor bank requires a separate set of switches, making its construction less economical. From Fig. 9: di Lcom += v Vsin t (13) dt cm t Fig. 8 Waveforms of reactive powers. where , icom is the current through the compensator and vc is the voltage across the capacitor. qL – Reactive power drawn by load. qcom – Reactive power supplied by compensator. dvc q – Resultant reactive power flowing on the iCcom = (14) S dt transmission line after compensation. It is given as: dv2 q=+ q q (12) LCc += v Vsin t (15) S L com dt 2 cm 2 d vcm1 V 2 +=vtc sin dt LC LC (16) DOI: http://dx.doi.org/10.24018/ejers.2020.5.12.2253 Vol 5 | Issue 12 | December 2020 48 EJERS, European Journal of Engineering Research and Science Vol. 5, No. 12, December 2020 The solution of equation (16) can be found to be: where, Vm vc= Acos r t + B sin r t + 2 sin t 1 − LC CVm (17) x = 1 1 − 2 LC From equation (14): Vm sin xC2 =r 2 1− LC CVm i= − C Asin t + CB cos t + cos t x3 = r CV co com r r r r 1 − 2 LC (18) To improve the power factor, a TSC is switched on at the where, peak of the system voltage (i.e., when α = 90°).
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