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Modified static VAR compensator using a large value AC capacitor
Electric Power Systems Research 80 (2010) 240–247
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Modified static VAR compensator using a large value AC capacitor R. Mahanty ∗ Department of Electrical Engineering, Institute of Technology, Banaras Hindu University, Varanasi 221005, India
a r t i c l e
i n f o
Article history: Received 20 January 2009 Received in revised form 17 July 2009 Accepted 6 September 2009 Available online 9 October 2009 Keywords: Static VAR compensator (SVC) Reactive power compensation Shunt passive filter (SPF) Active power filter (APF)
a b s t r a c t To overcome some of the limitations of conventional static VAR compensators (SVCs) which are widely used for reactive power compensation, a modified SVC (MSVC) has been proposed. MSVC uses a large value AC capacitor. The large value AC capacitor is realized using unipolar DC capacitors and power semiconductor devices. Unlike the conventional SVCs, the proposed MSVC does not require additional shunt passive filters for harmonic filtering. MSVC has been verified through analysis and simulation. A practical implementation of MSVC has been realized and tested. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Static VAR compensator (SVC) using thyristor switched capacitor (TSC) and thyristor controlled inductor (TCI) schemes have traditionally been used for reactive power compensation [1–3]. TSC and TCI schemes have a major disadvantage that they generate current harmonics. Therefore, additional shunt passive filters (SPFs) are required to filter the harmonics. SPFs comprising of capacitor and inductor have been traditionally used to filter the harmonic currents generated by nonlinear loads. In SPFs, the value of capacitor and inductor are selected to offer minimum impedance at the tuned harmonic frequency. The low impedance path allows the selected harmonic current to flow through it. SPF can filter out one harmonic frequency effectively, for which it is tuned. In practical applications SPF have many disadvantages, such as, influence of source inductance on the compensation characteristics, series and parallel resonance with the source and the load, overloading of the SPFs with the increase in harmonic currents, requirement of different SPFs for filtering different harmonics and so on. Active power filters (APFs) have been widely investigated [4–11] to overcome the limitations of SPFs. APFs are also used for reactive power compensation in addition to harmonic filtering. APFs are effective for small nonlinear loads, but are not feasible and cost effective for large rated nonlinear loads. Their installation and running costs are high, since they require high performance voltage (or current) source inverters. Hybrid APFs can improve the com-
∗ Tel.: +91 542 2575388. E-mail address: [email protected]. 0378-7796/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2009.09.008
pensation characteristics of SPFs with smaller rated APFs [12–17]. However, implementation of a hybrid APF system typically requires a high bandwidth pulse width modulated inverter. Hence, applications of the existing hybrid APF systems are also limited up to a certain power range of nonlinear loads. For higher rated nonlinear loads; TSC, TCI and SPF are still used for reactive power compensation and harmonic filtering. SPF using a large value AC capacitor has been reported to overcome the limitations of conventional SPFs [18]. It comprises of a series and parallel tuned LC tank circuit. DC capacitors and power semiconductor devices have been used in the said SPF to realize large value AC capacitor. In contrast to AC capacitors, DC capacitors are available in higher values at nominal supply voltages and above. Among the DC capacitors, aluminium electrolytic and metallized polypropylene DC link capacitors are available in higher values at nominal supply voltages and above. However, the aluminium electrolytic capacitors of higher capacitance values have significantly lower current rating, high equivalent series resistance (RESR ) and high self inductance (LESL ) [19]. Where as, the metallized polypropylene DC link capacitors of higher capacitance values are available in higher current ratings and have low RESR and LESL [20] compared to aluminium electrolytic capacitors. In this work, the conventional SVC has been modified for harmonic filtering in addition to reactive power compensation with only one additional inductor in series with the large value AC capacitor. The large value AC capacitor along with the inductor forms the SPF which not only filters the harmonics generated by the TCI but also the harmonics present in the line. When the capacitance value is large in SPF, it filters out several harmonics with only one set of SPF tuned at lowest harmonic frequency [18].
R. Mahanty / Electric Power Systems Research 80 (2010) 240–247
Fig. 3. Proposed MSVC circuit.
Fig. 1. Conceptual circuit for realizing an AC capacitor using two DC capacitors.
2. AC capacitor using two DC capacitors An AC capacitor has been reported using two DC capacitors and two diodes [21]. This AC capacitor has been used in the output filter of a single-phase voltage regulator circuit where it works satisfactorily. However in this AC capacitor circuit, the DC capacitors are not allowed to discharge if AC voltage is applied across it. In the present work the two switches allow to discharge the DC capacitors. The conceptual circuit for realizing an AC capacitor using two DC capacitors is shown in Fig. 1 [18]. The circuit uses two DC capacitors, C1 and C2; two power diodes, D1 and D2; and two power semiconductor switches, S1 and S2. Operation modes of the proposed AC capacitor can be explained with the help of Fig. 2. The capacitor voltage and current are denoted by vC and iC respectively in Fig. 2. The operation of the circuit can be described in four modes. • Mode 1 (t0 –t1 ): During the first quarter voltage cycle, current flows through C1 and D1. Capacitor C1 charges to the peak supply voltage at the end of this interval at t1 . Capacitor C2 experiences a small reverse voltage equal to the forward voltage drop of diode D1. The small reverse voltage is well within the specified negative voltage limit of the DC capacitor C2. This is important since the DC capacitors have very small negative voltage limit (1–2 V). Gate pulse is applied to the switch S1 at the beginning of mode 1 at t0 . However, the switch S1 starts conducting at the beginning of the next quarter cycle at t1 only. This is done in order to avoid any turn-on delay of the switch S1. • Mode 2 (t1 –t2 ): Switch S1 starts conducting at the beginning of this interval at t1 . Capacitor C1 starts discharging through the source and switch S1. The voltage across C1 follows the supply voltage and becomes zero at the end of this interval at t2 . S1 is turned off at t2 . In order to perform the switching exactly at t2 , the gate pulse is removed a bit earlier depending on the turn-off time of the switch. • Mode 3 (t2 –t3 ): This mode of operation is similar to mode 1 in the negative direction. At the beginning of this interval, C2 and
Fig. 2. Operation modes of the proposed AC capacitor.
241
D2 start conducting and the capacitor C2 is charged to the negative peak of the supply voltage at t3 . Capacitor C1 experiences a small reverse voltage equal to the forward voltage drop of diode D2. Gate pulse is applied to S2 at the beginning of mode 3 at t2 . However, the switch S2 starts conducting at the beginning of the next quarter cycle at t3 only. • Mode 4 (t3 –t4 ): Operation of this mode is similar to mode 2 in the negative direction. Capacitor C2 discharges in this interval through the source and switch S2. The voltage across C2 follows the supply voltage. S2 is turned off at t4 . Combining the four modes, it is observed that the two DC capacitors working together behave as an AC capacitor. 3. Modified SVC In power distribution system reactive power compensation needed is usually of the order of hundreds of kVAR. As large value AC capacitors are not available, a large number of AC capacitors are connected in parallel to meet the VAR demand. The large value AC capacitor has been used in modified SVC (MSVC) for reactive power compensation and harmonic filtering. The circuit of MSVC is shown in Fig. 3. The waveforms of vL1 (voltage across L1) and iL1 (current through L1) are shown in Fig. 4. The large value AC capacitor C (realized by C1, C2; D1, D2; and S1, S2) provides the leading VARs. The current through inductor L1 is controlled by back-to-back connected thyristors, allowing the circuit to supply the necessary lagging VAR depending upon the requirement. The SPF formed by the combination of C and L2 filters out the harmonics generated by the thyristor controlled inductor L1 and also the harmonics present in the line. 3.1. Theory of operation of MSVC The mathematical expressions for MSVC for reactive power compensation and harmonic filtering are derived in this section (L1 = L1 and L2 = L2 in the equations given in this section).
Fig. 4. Waveforms of vL1 and iL1 .
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The instantaneous source voltage can be represented as √ vs = 2Vs cos ωt.
(1)
The rms value of fundamental component of current flowing through the inductor L1 is given by IL1 =
Vs (2 − 2˛ + sin 2˛) ωL1
≤ ˛ ≤ . 2
(2)
where ˛ is the thyristor delay angle. As the current through L1 is lagging the voltage vs by 90◦ , ˛ has no control from 0◦ to 90◦ . Effective inductance of L1 is given by Leff =
Vs L1 = ωIL1 2 − 2˛ + sin 2˛
≤ ˛ ≤ . 2
(3)
Effective susceptance of L1 is given by Beff =
1 2 − 2˛ + sin 2˛ = ωLeff ωL1
Fig. 5. Impedance versus frequency response plots of the SPF.
/2 ≤ ˛ ≤ .
(4) Substituting the value of IL1 from (2) into (9)
Vs2 Leading VAR supplied by MSVC = . ((1/ωC) − ωL2 )
(5)
Lagging VAR supplied by MSVC = Vs · IL1 .
(6)
Therefore, net leading VAR supplied by the MSVC is given by QMSVC =
Vs2 − Vs · IL1 . ((1/ωC) − ωL2 )
(7)
Larger the capacitor size, higher will be the value of QMSVC which results into higher power rating of MSVC. The lagging VAR of the system load is given by QL = Vs Is sin
(8)
where is the power factor angle. The lagging VAR of the system load (QL ) and leading VAR supplied by the MSVC (QMSVC ) are equal at unity power factor condition. Equating (7) and (8) for this condition gives IL1 =
Vs − Is sin . ((1/ωC) − ωL2 )
(9)
Vs (2 − 2˛ + sin 2˛) Vs = − Is sin . ωL1 ((1/ωC) − ωL2 )
(10)
For fixed supply voltage Vs and for a fixed value of C, L1 and L2 , (10) relates reactive current Is sin and firing angle ˛. Thus the reactive current can be controlled by controlling the ˛ of the thyristors. For a required value of QMSVC , first the DC capacitor values are assumed for realization of large value AC capacitor C. The value of L2 is so selected that the combination C and L2 are tuned at the lowest harmonic frequency. The value of L1 is selected to satisfy the relation ((1/ωC) − ωL2 ) = ωL1 , so that, when the load is purely resistive, capacitive reactance is equal to the inductive reactance. This can be achieved by making the thyristor firing angle of TCI zero. The SPF formed by C and L2 provides path for the harmonic currents. The importance of large value capacitance in the SPF can be explained by the impedance versus frequency response plots of the SPF shown in Fig. 5. Traces 1–3 show plots of the SPF tuned at third harmonic frequency (C1 = C2 = 1000 F and L2 = 1.27 mH for trace 1; C1 = C2 = 1500 F and L2 = 0.84 mH for trace 2; and C1 = C2 = 2000 F
Fig. 6. Single-phase MSVC.
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Fig. 7. Simulated waveforms of single-phase MSVC: (a) load current I(RL), (b) source current I(Ls) and voltage at node 1 V(1), (c) capacitor currents I(C1) and I(C2) and (d) capacitor voltages V(2)–V(3) and V(3)–V(4).
and L2 = 0.63 mH for trace 3). Traces 4–6 show the plots of the harmonic filter tuned at the fifth harmonic frequency (C1 = C2 = 500 F and L2 = 0.84 mH for trace 4; C1 = C2 = 750 F and L2 = 0.56 mH for trace 5; and C1 = C2 = 1000 F and L2 = 0.42 mH for trace 6). Trace 7 shows plot of a conventional SPF tuned at third harmonic frequency having an AC capacitor of 50 F and inductor of 22.5 mH. Trace 8 shows the plot of source impedance (Ls = 2 mH and Rs = 0.1 ). From the impedance versus frequency response plots of Fig. 5, it is evident that larger the value of the capacitance in SPF, better is the filtering effect. In this way, using a large value of AC capacitors in MSVC, it can provide large amount of leading vars. MSVC does not require additional SPFs for filtering the harmonics generated by the TCI. Moreover, MSVC also filters the other harmonics present in the system. For large capacitance value, a large amount of fundamental current flows through C and L2, which would lead to larger size of L2 and, consequently, an increase in the cost of the proposed MSVC. However, the advantage of MSVC as compared to conventional SVC is that the former does not require a large number of capacitors connected in parallel for large reactive power compensation. Moreover, unlike the conventional SVC, the MSVC does not require additional SPFs to filter the harmonics generated by it.
4. Simulation circuit of MSVC The performance of MSVC is verified through simulation of single-phase and three-phase MSVC circuits. 4.1. Single-phase MSVC The single-phase MSVC for a 230 V, 50 Hz AC supply is shown in Fig. 6. The load used is a combination of linear (RL load) and nonlinear load (diode rectifier feeding an RL load). The DC capacitors (C1 and C2) values used are 2500 F. Fig. 7 shows simulated waveforms of single-phase MSVC. Fig. 7(a) shows the waveform of load current I(RL). Fig. 7(b) shows the waveforms of source current I(Ls) and voltage at node 1 V(1). Fig. 7(c) shows the waveforms of capacitor currents I(C1) and I(C2). Fig. 7(d) shows the capacitor voltages V(2)–V(3) and V(3)–V(4). Combining V(2)–V(3) and V(3)–V(4), the voltage across the equivalent AC capacitor is obtained. The dynamic response of the MSVC can be observed from Fig. 7 (b). Fig. 8(a)–(c) show the harmonic spectra of the waveforms of I(RL), I(Ls) and voltage at point of common coupling (PCC) V(2). From the harmonic spectra, it is calculated that the total harmonic distortions (THDs) of I(RL) is 23.505%, I(Ls) is 1.737% and V(2) is 4.739%.
Fig. 8. Harmonic spectra of the simulated waveforms of single-phase MSVC: (a) load current I(RL), (b) source current I(Ls) and (c) voltage at PCC V(2).
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Fig. 9. Three-phase MSVC.
It may be observed from Fig. 7(b) that the source current I(Ls) contains harmonics and lags the voltage V(1) before switching on the MSVC. After switching on the MSVC (at 300 ms), I(Ls) becomes sinusoidal as well as in phase with V(1). Hence the proposed MSVC is performing both reactive power compensation and harmonic
filtering. On the contrary, the conventional SVC requires a large number of AC capacitors connected in parallel when the reactive power to be compensated is large. Also, additional SPFs are required to filter the harmonics generated by TCI. The voltage quality issues, such as, voltage sag and voltage flicker are mitigated
Fig. 10. Simulated waveforms of three-phase MSVC: (a) load currents in the three phases I(RL1), I(RL2) and I(RL3), (b) source currents in the three phases I(Ls1), I(Ls2) and I(Ls3), (c) capacitor currents I(C1) and I(C2) of phase 1 and (d) capacitor voltages V(2)–V(3) and V(3)–V(4) of phase 1.
R. Mahanty / Electric Power Systems Research 80 (2010) 240–247
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Fig. 11. Schematic block diagram for generating firing pulses of thyristors T1 and T2.
by the proposed MSVC in the same way as done by conventional SVCs.
4.2. Three-phase MSVC The three-phase MSVC is shown in Fig. 9. The dynamic response of the three-phase MSVC is found similar to the single-phase MSVC. Fig. 10 shows the simulated waveforms under steady state for this case. Fig. 10(a) shows the load currents in the three phases I(RL1), I(RL2) and I(RL3). Fig. 10(b) shows the source currents in the three phases I(Ls1), I(Ls2) and I(Ls3). Fig. 10(c) shows capacitor currents I(C1) and I(C2) of phase 1. Fig. 10(d) shows the capacitor voltages V(2)–V(3) and V(3)–V(4) of phase 1.
5. Experimental verifications A 30 kVA, single-phase MSVC has been experimentally verified for a 230 V, 50 Hz supply. The circuit shown in Fig. 6 for singlephase MSVC has been used in the experimental set up. Two 2500 F metallized polypropylene DC link capacitors C1 and C2 are used to realize a 2500 F AC capacitor. The schematic block diagram for generating firing pulses of thyristors T1 and T2 is shown in Fig. 11. The 8085 microprocessor is used for generating the delays. The source current is sensed at every negative zero crossing of the supply voltage using the zero crossing detector realized by LM311. The current obtained gives the value of reactive current Is sin at that instant. The firing angle ˛ of the thyristors to make the power factor unity is calculated using
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Fig. 14. Experimental source voltage and current waveforms without connecting MSVC.
Fig. 12. Flow chart of the main program.
(10) by the microprocessor. Counter 8253, logic gates and other analog and digital circuits are used to obtain the firing pulses for thyristors. The phase locked loop (PLL) is used minimize the effect of any change in the supply frequency. The counter 8253 clock frequency is maintained at 51.2 kHz by voltage controlled oscillator. The flow chart of main program and interrupt service subroutine are shown in Figs. 12 and 13 respectively. The source voltage and current waveforms without connecting the MSVC are shown in Fig. 14. The harmonic spectrum of the source current without connecting the MSVC is shown in Fig. 15. The THD of the source current is 15.746%. The source current is lagging the source voltage and the measured power factor is 0.745 (lagging). Source voltage and current waveforms after connecting MSVC are
Fig. 13. Flow chart of interrupt service routine.
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the MSVC, the THD of the source current and voltage at PCC can be reduced to less than 5% by the proposed MSVC having only one set of SPF tuned at third harmonic frequency. This is a major advantage of MSVC over conventional SVCs in which different sets of SPFs tuned at different harmonic frequencies are required for filtering different harmonic frequency currents. Since the MSVC does not require high performance complex inverters as required in conventional APFs, it can be used in higher power applications than conventional APFs. Fig. 15. Experimental source current harmonic spectrum without connecting MSVC.
Fig. 16. Experimental source voltage and current waveforms after connecting MSVC.
Fig. 17. Experimental source current harmonic spectrum after connecting MSVC.
shown in Fig. 16. The harmonic spectrum of source current after connecting MSVC is shown in Fig. 17. It is observed that the THD of the source current after connecting MSVC is reduced to 1.638% and the power factor has improved to 0.981 (lagging). 6. Conclusion MSVC has been proposed for reactive power compensation using a large value AC capacitor. The large value AC capacitor has been realized using two large value DC capacitors and power semiconductor devices. Simulation and experimental results establish that with a large value of capacitance (of the order of 2500 F) in
References [1] L. Gyugyi, Reactive power generation and control by thyristor circuits, IEEE Trans. Ind. Appl. 15 (5) (1979) 521–532. [2] L. Gyugyi, E.R. Taylor Jr., Characteristics of static, thyristor-controlled shunt compensators for power transmission system applications, IEEE Trans. Power Apparatus Syst. 99 (5) (1980) 1795–1804. [3] H. Jin, G. Goós, L. Lopes, An efficient switched-reactor-based static VAR compensator, IEEE Trans. Ind. Appl. 30 (4) (1994) 998–1005. [4] B. Singh, V. Verma, Selective compensation of power-quality problems through active filter by current decomposition, IEEE Trans. Power Deliv. 23 (2) (2008) 792–799. [5] M. Routimo, M. Salo, H. Tuusa, Comparison of voltage-source and currentsource shunt active power filters, IEEE Trans. Power Electron. 22 (2) (2007) 636–643. [6] M.I.M. Montero, E.R. Cadaval, F.B. González, Comparison of control strategies for shunt active power filters in three-phase four-wire systems, IEEE Trans. Power Electron. 22 (1) (2007) 229–236. [7] G.K. Singh, A.K. Singh, R. Mitra, A simple fuzzy logic based robust active power filter for harmonics minimization under random load variation, Elect. Power Syst. Res. 77 (8) (2007) 1101–1111. [8] M. Kale, E. Özdemir, Harmonic and reactive power compensation with shunt active power filter under non-ideal mains voltage, Elect. Power Syst. Res. 74 (3) (2005) 363–370. [9] M.C. Benhabib, S. Saadate, New control approach for four-wire active power filter based on the use of synchronous reference frame, Elect. Power Syst. Res. 73 (3) (2005) 353–362. [10] M. Basu, S.P. Das, G.K. Dubey, Parallel converter scheme for high-power active power filters, IEE Proc. Electr. Power Appl. 151 (4) (2004) 460–466. [11] G. Casaravilla, A. Salvia, C. Briozzo, E. Watanabe, Control strategies of selective harmonic current shunt active filter, IEE Proc. Gen. Transm. Distrib. 149 (6) (2002) 689–694. [12] W.L. Jou, J.C. Wu, K.D. Wu, C.H. Li, W.P. Hsu, Novel configuration for three-phase hybrid power filter, Elect. Power Syst. Res. 78 (7) (2008) 1153–1160. [13] B. Singh, V. Verma, An indirect current control of hybrid power filter for varying loads, IEEE Trans. Power Deliv. 21 (1) (2006) 178–184. [14] S. Kim, P.N. Enjeti, A new hybrid active power filter (APF) topology, IEEE Trans. Power Electron. 17 (1) (2002) 48–54. [15] P.T. Cheng, S. Bhattacharya, D.M. Divan, Control of square-wave inverters in high-power hybrid active filter systems, IEEE Trans. Ind. Appl. 34 (3) (1998) 458–472. [16] S. Bhattacharya, P.T. Cheng, D.M. Divan, Hybrid solutions for improving passive filter performance in high power applications, IEEE Trans. Ind. Appl. 33 (3) (1997) 732–747. [17] M. Rastogi, N. Mohan, A.A. Edris, Hybrid-active filtering of harmonic currents in power system, IEEE Trans. Power Deliv. 10 (4) (1995) 1994–2000. [18] R. Mahanty, A.K. Kapoor, Quasi-passive filter for harmonic filtering, Elect. Power Syst. Res. 78 (8) (2008) 1456–1465. [19] http://www.alconelectronics.com. [20] http://www.icar.it/NewIcar/epotenza/pdf/lnk new.pdf. [21] H.W. Park, S.J. Park, J.G. Park, C.U. Kim, A novel high-performance voltage regulator for single-phase ac sources, IEEE Trans. Ind. Electron. 48 (3) (2001) 554–562.
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Modified static VAR compensator using a large value AC capacitor R. Mahanty ∗ Department of Electrical Engineering, Institute of Technology, Banaras Hindu University, Varanasi 221005, India
a r t i c l e
i n f o
Article history: Received 20 January 2009 Received in revised form 17 July 2009 Accepted 6 September 2009 Available online 9 October 2009 Keywords: Static VAR compensator (SVC) Reactive power compensation Shunt passive filter (SPF) Active power filter (APF)
a b s t r a c t To overcome some of the limitations of conventional static VAR compensators (SVCs) which are widely used for reactive power compensation, a modified SVC (MSVC) has been proposed. MSVC uses a large value AC capacitor. The large value AC capacitor is realized using unipolar DC capacitors and power semiconductor devices. Unlike the conventional SVCs, the proposed MSVC does not require additional shunt passive filters for harmonic filtering. MSVC has been verified through analysis and simulation. A practical implementation of MSVC has been realized and tested. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Static VAR compensator (SVC) using thyristor switched capacitor (TSC) and thyristor controlled inductor (TCI) schemes have traditionally been used for reactive power compensation [1–3]. TSC and TCI schemes have a major disadvantage that they generate current harmonics. Therefore, additional shunt passive filters (SPFs) are required to filter the harmonics. SPFs comprising of capacitor and inductor have been traditionally used to filter the harmonic currents generated by nonlinear loads. In SPFs, the value of capacitor and inductor are selected to offer minimum impedance at the tuned harmonic frequency. The low impedance path allows the selected harmonic current to flow through it. SPF can filter out one harmonic frequency effectively, for which it is tuned. In practical applications SPF have many disadvantages, such as, influence of source inductance on the compensation characteristics, series and parallel resonance with the source and the load, overloading of the SPFs with the increase in harmonic currents, requirement of different SPFs for filtering different harmonics and so on. Active power filters (APFs) have been widely investigated [4–11] to overcome the limitations of SPFs. APFs are also used for reactive power compensation in addition to harmonic filtering. APFs are effective for small nonlinear loads, but are not feasible and cost effective for large rated nonlinear loads. Their installation and running costs are high, since they require high performance voltage (or current) source inverters. Hybrid APFs can improve the com-
∗ Tel.: +91 542 2575388. E-mail address: [email protected]. 0378-7796/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2009.09.008
pensation characteristics of SPFs with smaller rated APFs [12–17]. However, implementation of a hybrid APF system typically requires a high bandwidth pulse width modulated inverter. Hence, applications of the existing hybrid APF systems are also limited up to a certain power range of nonlinear loads. For higher rated nonlinear loads; TSC, TCI and SPF are still used for reactive power compensation and harmonic filtering. SPF using a large value AC capacitor has been reported to overcome the limitations of conventional SPFs [18]. It comprises of a series and parallel tuned LC tank circuit. DC capacitors and power semiconductor devices have been used in the said SPF to realize large value AC capacitor. In contrast to AC capacitors, DC capacitors are available in higher values at nominal supply voltages and above. Among the DC capacitors, aluminium electrolytic and metallized polypropylene DC link capacitors are available in higher values at nominal supply voltages and above. However, the aluminium electrolytic capacitors of higher capacitance values have significantly lower current rating, high equivalent series resistance (RESR ) and high self inductance (LESL ) [19]. Where as, the metallized polypropylene DC link capacitors of higher capacitance values are available in higher current ratings and have low RESR and LESL [20] compared to aluminium electrolytic capacitors. In this work, the conventional SVC has been modified for harmonic filtering in addition to reactive power compensation with only one additional inductor in series with the large value AC capacitor. The large value AC capacitor along with the inductor forms the SPF which not only filters the harmonics generated by the TCI but also the harmonics present in the line. When the capacitance value is large in SPF, it filters out several harmonics with only one set of SPF tuned at lowest harmonic frequency [18].
R. Mahanty / Electric Power Systems Research 80 (2010) 240–247
Fig. 3. Proposed MSVC circuit.
Fig. 1. Conceptual circuit for realizing an AC capacitor using two DC capacitors.
2. AC capacitor using two DC capacitors An AC capacitor has been reported using two DC capacitors and two diodes [21]. This AC capacitor has been used in the output filter of a single-phase voltage regulator circuit where it works satisfactorily. However in this AC capacitor circuit, the DC capacitors are not allowed to discharge if AC voltage is applied across it. In the present work the two switches allow to discharge the DC capacitors. The conceptual circuit for realizing an AC capacitor using two DC capacitors is shown in Fig. 1 [18]. The circuit uses two DC capacitors, C1 and C2; two power diodes, D1 and D2; and two power semiconductor switches, S1 and S2. Operation modes of the proposed AC capacitor can be explained with the help of Fig. 2. The capacitor voltage and current are denoted by vC and iC respectively in Fig. 2. The operation of the circuit can be described in four modes. • Mode 1 (t0 –t1 ): During the first quarter voltage cycle, current flows through C1 and D1. Capacitor C1 charges to the peak supply voltage at the end of this interval at t1 . Capacitor C2 experiences a small reverse voltage equal to the forward voltage drop of diode D1. The small reverse voltage is well within the specified negative voltage limit of the DC capacitor C2. This is important since the DC capacitors have very small negative voltage limit (1–2 V). Gate pulse is applied to the switch S1 at the beginning of mode 1 at t0 . However, the switch S1 starts conducting at the beginning of the next quarter cycle at t1 only. This is done in order to avoid any turn-on delay of the switch S1. • Mode 2 (t1 –t2 ): Switch S1 starts conducting at the beginning of this interval at t1 . Capacitor C1 starts discharging through the source and switch S1. The voltage across C1 follows the supply voltage and becomes zero at the end of this interval at t2 . S1 is turned off at t2 . In order to perform the switching exactly at t2 , the gate pulse is removed a bit earlier depending on the turn-off time of the switch. • Mode 3 (t2 –t3 ): This mode of operation is similar to mode 1 in the negative direction. At the beginning of this interval, C2 and
Fig. 2. Operation modes of the proposed AC capacitor.
241
D2 start conducting and the capacitor C2 is charged to the negative peak of the supply voltage at t3 . Capacitor C1 experiences a small reverse voltage equal to the forward voltage drop of diode D2. Gate pulse is applied to S2 at the beginning of mode 3 at t2 . However, the switch S2 starts conducting at the beginning of the next quarter cycle at t3 only. • Mode 4 (t3 –t4 ): Operation of this mode is similar to mode 2 in the negative direction. Capacitor C2 discharges in this interval through the source and switch S2. The voltage across C2 follows the supply voltage. S2 is turned off at t4 . Combining the four modes, it is observed that the two DC capacitors working together behave as an AC capacitor. 3. Modified SVC In power distribution system reactive power compensation needed is usually of the order of hundreds of kVAR. As large value AC capacitors are not available, a large number of AC capacitors are connected in parallel to meet the VAR demand. The large value AC capacitor has been used in modified SVC (MSVC) for reactive power compensation and harmonic filtering. The circuit of MSVC is shown in Fig. 3. The waveforms of vL1 (voltage across L1) and iL1 (current through L1) are shown in Fig. 4. The large value AC capacitor C (realized by C1, C2; D1, D2; and S1, S2) provides the leading VARs. The current through inductor L1 is controlled by back-to-back connected thyristors, allowing the circuit to supply the necessary lagging VAR depending upon the requirement. The SPF formed by the combination of C and L2 filters out the harmonics generated by the thyristor controlled inductor L1 and also the harmonics present in the line. 3.1. Theory of operation of MSVC The mathematical expressions for MSVC for reactive power compensation and harmonic filtering are derived in this section (L1 = L1 and L2 = L2 in the equations given in this section).
Fig. 4. Waveforms of vL1 and iL1 .
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The instantaneous source voltage can be represented as √ vs = 2Vs cos ωt.
(1)
The rms value of fundamental component of current flowing through the inductor L1 is given by IL1 =
Vs (2 − 2˛ + sin 2˛) ωL1
≤ ˛ ≤ . 2
(2)
where ˛ is the thyristor delay angle. As the current through L1 is lagging the voltage vs by 90◦ , ˛ has no control from 0◦ to 90◦ . Effective inductance of L1 is given by Leff =
Vs L1 = ωIL1 2 − 2˛ + sin 2˛
≤ ˛ ≤ . 2
(3)
Effective susceptance of L1 is given by Beff =
1 2 − 2˛ + sin 2˛ = ωLeff ωL1
Fig. 5. Impedance versus frequency response plots of the SPF.
/2 ≤ ˛ ≤ .
(4) Substituting the value of IL1 from (2) into (9)
Vs2 Leading VAR supplied by MSVC = . ((1/ωC) − ωL2 )
(5)
Lagging VAR supplied by MSVC = Vs · IL1 .
(6)
Therefore, net leading VAR supplied by the MSVC is given by QMSVC =
Vs2 − Vs · IL1 . ((1/ωC) − ωL2 )
(7)
Larger the capacitor size, higher will be the value of QMSVC which results into higher power rating of MSVC. The lagging VAR of the system load is given by QL = Vs Is sin
(8)
where is the power factor angle. The lagging VAR of the system load (QL ) and leading VAR supplied by the MSVC (QMSVC ) are equal at unity power factor condition. Equating (7) and (8) for this condition gives IL1 =
Vs − Is sin . ((1/ωC) − ωL2 )
(9)
Vs (2 − 2˛ + sin 2˛) Vs = − Is sin . ωL1 ((1/ωC) − ωL2 )
(10)
For fixed supply voltage Vs and for a fixed value of C, L1 and L2 , (10) relates reactive current Is sin and firing angle ˛. Thus the reactive current can be controlled by controlling the ˛ of the thyristors. For a required value of QMSVC , first the DC capacitor values are assumed for realization of large value AC capacitor C. The value of L2 is so selected that the combination C and L2 are tuned at the lowest harmonic frequency. The value of L1 is selected to satisfy the relation ((1/ωC) − ωL2 ) = ωL1 , so that, when the load is purely resistive, capacitive reactance is equal to the inductive reactance. This can be achieved by making the thyristor firing angle of TCI zero. The SPF formed by C and L2 provides path for the harmonic currents. The importance of large value capacitance in the SPF can be explained by the impedance versus frequency response plots of the SPF shown in Fig. 5. Traces 1–3 show plots of the SPF tuned at third harmonic frequency (C1 = C2 = 1000 F and L2 = 1.27 mH for trace 1; C1 = C2 = 1500 F and L2 = 0.84 mH for trace 2; and C1 = C2 = 2000 F
Fig. 6. Single-phase MSVC.
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Fig. 7. Simulated waveforms of single-phase MSVC: (a) load current I(RL), (b) source current I(Ls) and voltage at node 1 V(1), (c) capacitor currents I(C1) and I(C2) and (d) capacitor voltages V(2)–V(3) and V(3)–V(4).
and L2 = 0.63 mH for trace 3). Traces 4–6 show the plots of the harmonic filter tuned at the fifth harmonic frequency (C1 = C2 = 500 F and L2 = 0.84 mH for trace 4; C1 = C2 = 750 F and L2 = 0.56 mH for trace 5; and C1 = C2 = 1000 F and L2 = 0.42 mH for trace 6). Trace 7 shows plot of a conventional SPF tuned at third harmonic frequency having an AC capacitor of 50 F and inductor of 22.5 mH. Trace 8 shows the plot of source impedance (Ls = 2 mH and Rs = 0.1 ). From the impedance versus frequency response plots of Fig. 5, it is evident that larger the value of the capacitance in SPF, better is the filtering effect. In this way, using a large value of AC capacitors in MSVC, it can provide large amount of leading vars. MSVC does not require additional SPFs for filtering the harmonics generated by the TCI. Moreover, MSVC also filters the other harmonics present in the system. For large capacitance value, a large amount of fundamental current flows through C and L2, which would lead to larger size of L2 and, consequently, an increase in the cost of the proposed MSVC. However, the advantage of MSVC as compared to conventional SVC is that the former does not require a large number of capacitors connected in parallel for large reactive power compensation. Moreover, unlike the conventional SVC, the MSVC does not require additional SPFs to filter the harmonics generated by it.
4. Simulation circuit of MSVC The performance of MSVC is verified through simulation of single-phase and three-phase MSVC circuits. 4.1. Single-phase MSVC The single-phase MSVC for a 230 V, 50 Hz AC supply is shown in Fig. 6. The load used is a combination of linear (RL load) and nonlinear load (diode rectifier feeding an RL load). The DC capacitors (C1 and C2) values used are 2500 F. Fig. 7 shows simulated waveforms of single-phase MSVC. Fig. 7(a) shows the waveform of load current I(RL). Fig. 7(b) shows the waveforms of source current I(Ls) and voltage at node 1 V(1). Fig. 7(c) shows the waveforms of capacitor currents I(C1) and I(C2). Fig. 7(d) shows the capacitor voltages V(2)–V(3) and V(3)–V(4). Combining V(2)–V(3) and V(3)–V(4), the voltage across the equivalent AC capacitor is obtained. The dynamic response of the MSVC can be observed from Fig. 7 (b). Fig. 8(a)–(c) show the harmonic spectra of the waveforms of I(RL), I(Ls) and voltage at point of common coupling (PCC) V(2). From the harmonic spectra, it is calculated that the total harmonic distortions (THDs) of I(RL) is 23.505%, I(Ls) is 1.737% and V(2) is 4.739%.
Fig. 8. Harmonic spectra of the simulated waveforms of single-phase MSVC: (a) load current I(RL), (b) source current I(Ls) and (c) voltage at PCC V(2).
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Fig. 9. Three-phase MSVC.
It may be observed from Fig. 7(b) that the source current I(Ls) contains harmonics and lags the voltage V(1) before switching on the MSVC. After switching on the MSVC (at 300 ms), I(Ls) becomes sinusoidal as well as in phase with V(1). Hence the proposed MSVC is performing both reactive power compensation and harmonic
filtering. On the contrary, the conventional SVC requires a large number of AC capacitors connected in parallel when the reactive power to be compensated is large. Also, additional SPFs are required to filter the harmonics generated by TCI. The voltage quality issues, such as, voltage sag and voltage flicker are mitigated
Fig. 10. Simulated waveforms of three-phase MSVC: (a) load currents in the three phases I(RL1), I(RL2) and I(RL3), (b) source currents in the three phases I(Ls1), I(Ls2) and I(Ls3), (c) capacitor currents I(C1) and I(C2) of phase 1 and (d) capacitor voltages V(2)–V(3) and V(3)–V(4) of phase 1.
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Fig. 11. Schematic block diagram for generating firing pulses of thyristors T1 and T2.
by the proposed MSVC in the same way as done by conventional SVCs.
4.2. Three-phase MSVC The three-phase MSVC is shown in Fig. 9. The dynamic response of the three-phase MSVC is found similar to the single-phase MSVC. Fig. 10 shows the simulated waveforms under steady state for this case. Fig. 10(a) shows the load currents in the three phases I(RL1), I(RL2) and I(RL3). Fig. 10(b) shows the source currents in the three phases I(Ls1), I(Ls2) and I(Ls3). Fig. 10(c) shows capacitor currents I(C1) and I(C2) of phase 1. Fig. 10(d) shows the capacitor voltages V(2)–V(3) and V(3)–V(4) of phase 1.
5. Experimental verifications A 30 kVA, single-phase MSVC has been experimentally verified for a 230 V, 50 Hz supply. The circuit shown in Fig. 6 for singlephase MSVC has been used in the experimental set up. Two 2500 F metallized polypropylene DC link capacitors C1 and C2 are used to realize a 2500 F AC capacitor. The schematic block diagram for generating firing pulses of thyristors T1 and T2 is shown in Fig. 11. The 8085 microprocessor is used for generating the delays. The source current is sensed at every negative zero crossing of the supply voltage using the zero crossing detector realized by LM311. The current obtained gives the value of reactive current Is sin at that instant. The firing angle ˛ of the thyristors to make the power factor unity is calculated using
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Fig. 14. Experimental source voltage and current waveforms without connecting MSVC.
Fig. 12. Flow chart of the main program.
(10) by the microprocessor. Counter 8253, logic gates and other analog and digital circuits are used to obtain the firing pulses for thyristors. The phase locked loop (PLL) is used minimize the effect of any change in the supply frequency. The counter 8253 clock frequency is maintained at 51.2 kHz by voltage controlled oscillator. The flow chart of main program and interrupt service subroutine are shown in Figs. 12 and 13 respectively. The source voltage and current waveforms without connecting the MSVC are shown in Fig. 14. The harmonic spectrum of the source current without connecting the MSVC is shown in Fig. 15. The THD of the source current is 15.746%. The source current is lagging the source voltage and the measured power factor is 0.745 (lagging). Source voltage and current waveforms after connecting MSVC are
Fig. 13. Flow chart of interrupt service routine.
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the MSVC, the THD of the source current and voltage at PCC can be reduced to less than 5% by the proposed MSVC having only one set of SPF tuned at third harmonic frequency. This is a major advantage of MSVC over conventional SVCs in which different sets of SPFs tuned at different harmonic frequencies are required for filtering different harmonic frequency currents. Since the MSVC does not require high performance complex inverters as required in conventional APFs, it can be used in higher power applications than conventional APFs. Fig. 15. Experimental source current harmonic spectrum without connecting MSVC.
Fig. 16. Experimental source voltage and current waveforms after connecting MSVC.
Fig. 17. Experimental source current harmonic spectrum after connecting MSVC.
shown in Fig. 16. The harmonic spectrum of source current after connecting MSVC is shown in Fig. 17. It is observed that the THD of the source current after connecting MSVC is reduced to 1.638% and the power factor has improved to 0.981 (lagging). 6. Conclusion MSVC has been proposed for reactive power compensation using a large value AC capacitor. The large value AC capacitor has been realized using two large value DC capacitors and power semiconductor devices. Simulation and experimental results establish that with a large value of capacitance (of the order of 2500 F) in
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