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swell compensator and phase shifter based on Ćuk B2 matrix-reactance chopper
Electric Power Systems Research 125 (2015) 203–210
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Three-phase AC/AC converter for voltage sag/swell compensator and ´ B2 matrix-reactance chopper phase shifter based on Cuk Jacek Kaniewski ∗ University of Zielona Góra, Institute of Electrical Engineering, Zielona Góra, Poland
a r t i c l e
i n f o
Article history: Received 19 November 2014 Received in revised form 13 March 2015 Accepted 11 April 2015 Available online 25 May 2015 Keywords: Power quality Voltage sag/swell compensator Phase shifter Power flow control Bipolar matrix-reactance chopper AC/AC converter
a b s t r a c t This paper proposes a new topology for an AC/AC converter without DC energy storage to compensate deep voltage sags and swells and to control the output voltage phase shift. The analyzed topology is based ´ on an AC/AC CukB2 bipolar matrix-reactance chopper. The proposed solution is intended to protect sensitive loads and energy flow control in the AC power grid. The main advantage of the proposed solution is the combination of the properties of a series AC voltage compensator and phase shifters without DC energy storage. The presented AC/AC voltage converter is able to compensate single phase voltage interrupts, three-phase up to 50% voltage sags and swells, and change the phase of output voltage simultaneously and independently in relation to the input voltage. The paper presents an operational description, theoretical analysis and the experimental test results from a 1 kVA laboratory model using a PWM control strategy with open feedback loop. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The parameters of electric energy and its quality are very important, especially from the perspective of the end-user and sensitive loads connected to the grid. The parameters of electric energy are well known and described in [1]. Classification of voltage fluctuation depending on size of voltage change is shown in Fig. 1. Dynamic states in a power grid caused by faults, such as rapid load changes, turn-on/turn-off distribution generators, switching effects of renewable energy sources connected to the grid and atmospheric discharges generate undesirable effects for the end-user, such as voltage variations, voltage unbalance, voltage sags/swells (overvoltages), flicker effect or voltage interruption [2]. The analysis of power quality issues [3,4] shows that in about 92% of all power system events there are voltage sags with 40–50% of nominal value, and with a duration from 2 to 30 periods. Only about 4% of sags occur with a duration from 2 s to 10 min. In the case of AC voltage supply changes, both downward and upward, there is a high risk of damage to devices which are sensitive to voltage changes, for example: personal computers, transceiver devices, medical systems or faulty operation of other devices, such as, AC contactors, lighting loads, variable speed drives or industrial computers. In the case of big industrial plants and factories, voltage sags and swells may cause very large financial damages [5,6]. The application of
∗ Tel.: +48 68 328 2346; fax: +48 68 324 7293. E-mail address: [email protected] http://dx.doi.org/10.1016/j.epsr.2015.04.007 0378-7796/© 2015 Elsevier B.V. All rights reserved.
AC/AC converters using a Pulse Width Modulation (PWM) control strategy to construct secondary supply sources (voltage sag and swell compensators and voltage regulators) mitigate the unwanted effects of supply [7–17]. The AC/AC converters described in [7] are based on an AC/AC converter and operate without energy storage. However they are capable of compensating voltage sag only up to 50% of US “in-phase” with mode. This means that they cannot change the voltage phase angle. The solutions described in [8,9] provide good dynamic properties but are operated also only in an “in-phase” mode. The circuit described in [10] can control simultaneously voltage amplitude and phase. However, in order to realize these functions another four bidirectional switches in each phase are required. An often encountered circuit for voltage sag/swell compensation is the DVR (Dynamic Voltage Restorer) [11–15]. The conventional topologies of DVR are based on AC/DC/AC converters with DC energy storage. The DC energy storage unit is a part of the DVR which is both the most expensive part and susceptible to damage. The AC voltage compensator described in [16] operates only in an “in-phase” mode and is intended to compensate voltage perturbation such as voltage sags (deeper than 50% of nominal source voltage) and voltage swell (up to 140% of nominal source voltage). In this solution [16] is not capable of changing the phase of the output voltage. Modern AC power systems (smart grids) allow the connection of low power renewable energy sources (photo voltaic panels—PV, wind generators) to low voltage (LV) AC power systems. Renewable energy sources are connected to the grid by power electronic interfaces [17,18]. Voltage fluctuations in AC power systems can be caused by turning on and turning
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Fig. 1. Classification of voltage variation depending on size of change, UN —nominal supply voltage. ´ Fig. 3. Sinle-phase Cuk B2 matrix-reactance chopper.
2. Circuit and operation description off renewable energy sources connected to the grid, due to being dependent on the condition of the source energy (wind, sun, water flow, etc.). Consequently, this may lead to uncontrolled energy flow between the sources in an AC power grid. To eliminate uncontrolled energy flow in the AC power system such devices as phase shifters are used. The phase control of the line voltage in the power grid is one of the well-known methods for power flow control Eq. (1) and for transient stability in flexible AC transmission systems (FACTS) [19–21].
P=
US UL X
sin ,
(1)
where, US —source voltage, UL —load voltage, X—line reactance, ˚—angle of phase shift between US and UL . The classical phase shifter for power flow control in the AC power grid, based on an AC/AC converter is shown in Fig. 2. The various topologies of quadrature-booster phase shifters based on AC/AC converters are described in [22–24]. The main disadvantage of these solutions is that change of voltage amplitude depends on phase shifting (Fig. 2b). Moreover, often the change of the phase of output voltage is possible only in one direction [22–24]. The necessity to control the phase of voltage occurs not only in the case of power flow control Eq. (1) [22,23]. In the case of asymmetrical ungrounded short circuits in the AC power grid, fluctuation of both phase and amplitude of voltage parameters is caused. Having regard to the above, it is reasonable to construct devices with the ability to compensate simultaneously and independently voltage fluctuation and phase control of the AC line voltage. The paper presents a new topology of AC/AC converter destined to mitigate both voltage sags and swells and the phase of voltage fluctuation. Additionally presented is a solution with the ability to compensate single phase voltage interruptions and which operates without a DC energy storage. The described solution is an interesting alternative to conventional AC voltage sag/swell and interrupt compensators with DC energy storage.
´ uk B2 matrix-reactance choppers 2.1. AC/AC converter based on C The topology of the considered circuit of AC voltage sag/swell compensator with phase shifter function is based on the DVR concept. Used as a power electronic converter (in the described ´ solution) is a bipolar matrix-reactance chopper (MRC) Cuk B2 type with bidirectional switches S1 and S2 and input/output filters (Fig. 3). This converter is a direct AC/AC converter and operates without DC energy storage [25,26]. The idealized voltage transmittance understood as a voltage transform function and defined as the ratio of the output voltage value to the input voltage value of the MRC used (Fig. 3) is described by Eq. (2) and shown in Fig. 4a [25,26].
CukB2 U (1 − 2D) ´ H- U = U- 2 ≈ (1 − D) , -1
(2)
where, D—pulse duty factor defined as D = ton /TS , where TS —switching period, ton —turn-on time of switch S1. The idealized characteristic magnitude of voltage and phase of ´ voltage transmittance of Cuk B2 MRC as a function of pulse duty factor D are shown in Fig. 4a and b, respectively. As is shown in Fig. 4a for D < 0.5 the magnitude of voltage trans´ mittance is 1 > HU CukB2 > 0 and output voltage is in phase in relation to input voltage of MRC (Fig. 4b). Within this operational range ´ (D < 0.5, 1 > HU CukB2 > 0) the MRC operates with buck character. The phase of voltage transmittance is changed by for pulse duty factor ´ D > 0.5 (Fig. 4b). For D ≈ 0.67 the output voltage of MRC Cuk B2 (U2 ) is approximately equal to input voltage U1 , but is in the opposite ´ phase in relation to U1 . At operational range (D > 0.67, 1 < HU CukB2 ) ´ the MRC operates with boost character. The MRC Cuk B2 is called ´ a bipolar converter because the output voltage of the MRC Cuk B2 ´ could be changed in phase by . In the real circuit of a MRC Cuk B2 the useful working area is limited. Because of voltage transmittance, the input power factor rapidly decreases for D > 0.75 [16,17] and the useful working area should be limited from D = 0 to D = 0.75 (Fig. 4).
Fig. 2. Classical quadrature-booster phase shifter, (a) schematic, (b) voltage phasors.
J. Kaniewski / Electric Power Systems Research 125 (2015) 203–210
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Fig. 4. Idealized chatacteristic as a function of duty cycle D, (a) voltage transmittance, (b) phase of voltage transmittance.
The schematic diagram of the AC/AC converter used is based on ´ two single phase Cuk B2 MRCs and is shown in Fig. 5. The outputs of both MRCs (MRC 1 and MRC 2) are connected to the primary side of the transformers TR1 and TR2 , respectively. The secondary sides of TR1 and TR2 are connected in series (Fig. 5). The voltage ratio of TR1 and TR2 is equal 1 (nTR1 = nTR2 = n = 1). The both of matrix-reactance choppers are controlled via a simple PWM with a “dead time” control strategy (Fig. 5b). The output voltage of the AC/AC converter ´ (ucomp1 ) is the sum of output voltages of the particular Cuk B2 MRCs (uMRC1 , uMRC2 ) including the voltage ratio of the transformers (n)
L2 and L3. The output of AC/AC I converter (U1-U2) is connected in series between source and load (Fig. 6). Connected in an analogous way are the other AC/AC converters in phase L2 and L3. The source line voltages in a three-phase system are described as: Eqs. (3)–(5) j0 U - S1 = US × e ,
(3)
j U - S2 = US × e
−2 3
j U - S3 = US × e
2 3
,
(4)
,
(5)
2.2. Three-phase main circuit A simplified schematic diagram of the proposed voltage compensator for correcting sag/swell and control of voltage phase angle is shown in Fig. 6. As is shown in Fig. 6 the considered circuit contains three units of AC/AC converter (AC/AC I, AC/AC II and AC/AC III). Each module ´ of the AC/AC converter contains two single phase Cuk B2 MRCs in each phase (Fig. 5). The input connectors of the AC/AC converter operate in phase L1 (AC/AC I) are connected to connectors of phase
where, US is the maximum value of the amplitude of the source voltage in three-phase system (Fig. 6). Taking into account the idealized ´ voltage transmittance of the Cuk B2 matrix-reactance chopper Eq. (2), the idealized voltage transmittances of MRC1 and MRC2 are defined as Eqs. (6) and (7).
MRC1 U MRC1 (1 − 2D1 ) H U = , ≈
(6)
MRC2 U MRC2 (1 − 2D2 ) H U = , ≈
(7)
-
U - S2
-
(1 − D1 )
U - S3
(1 − D2 )
where, D1 and D2 —duty factor of MRC1 and MRC2, respectively. The duty factors (D1 and D2 ) of the MRC1 and MRC2 are controlled independently. Taking into account Eqs. (6) and (7) and the voltage ratio of TR1, TR2 (nTR1 = nTR2 = n = 1), the compensating voltage Ucomp1 for line L1 is a sum of output voltages nUMRC1 and nUMRC2 Eq. (8). U - comp1 = n × U - MRC1 + n × U - MRC2 = n×U - S2
(1 − 2D ) 1
(1 − D1 )
+n×U - S3
(1 − 2D ) 2
(1 − D2 )
.
(8)
With regard to the source line voltages Eqs. (3)–(5) the compensating voltage Eq. (8) can be described as Eq. (9):
j U - comp1 = n × US e
−2 3
×
(1 − 2D ) 1
(1 − D1 )
+ ej
2 3
×
(1 − 2D ) 2
(1 − D2 )
, (9)
Because the load voltage (UL ) of the considered circuit (Fig. 6) is a sum of source voltage US and compensating voltage Ucomp , then the load voltage for line L1 can by described as Eq. (10): U - L1 = U - S1 + U - comp1 = US × ej0 + n ´ Fig. 5. AC/AC converter based on two single-phase Cuk B2 MRCs, (a) main circuit, (b) simplify schematic block diagram of used PWM modulator.
× US ej
−2 3
×
(1 − 2D ) 1
(1 − D1 )
+ ej
2 3
×
(1 − 2D ) 2
(1 − D2 )
.
(10)
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J. Kaniewski / Electric Power Systems Research 125 (2015) 203–210
Fig. 6. Voltage sag/swell compensator with phase shifter function.
The voltage transmittance of the considered voltage compensator is given by Eq. (11). U - L1 H - U = US -
= ej0 + n × ej
−2 3
×
(1 − 2D ) 1
(1 − D1 )
+ ej
2 3
×
(1 − 2D ) 2
(1 − D2 )
. (11)
The diagrams of the voltage phasors of the considered circuit (Fig. 6), for different values of duty factors D1 and D2 , illustrating the principle of operation, are shown in Fig. 7 As can be seen (Fig. 7) it is possible to obtain an output voltage UL higher (Fig. 7a), lower (Fig. 7c and d), equal to (Fig. 7b), and in phase (Fig. 7a and c) or shifted in phase (Fig. 7b and d) in relation to the source voltage US . Because the voltage Ucomp1 (in line L1) is constructed from line voltages L2 and L3 it is possible to compensate single phase interrupt in line L1 (Fig. 7a). In this case MRC1 and MRC2 are operated with duty factor D1 = D2 = 0 (HU MRC1 = HU MRC2 = 1). Analogously is the case of voltage interrupt in phase L2 or L3. The compensation of voltage interruption is possible just in case single phase interrupts. 3. Simulation test results
(5 kHz) is a sort of compromise between commutation and conducting losses generated by power electronic switches. The resonant frequency (f0 ) of filters is set to about 1/3 of switching frequency (fS ).This condition (f0 = 1/3 fS ) is sufficient to obtain good filtration of higher harmonic components from the switching frequency. The voltage harmonic content (THDU ) is lower than 5%. The Idealized static characteristics of magnitude and phase of voltage transmittance of the considered circuit as a function of duty factors D1 and D2 are shown in Fig. 8. Simulation voltage waveforms in the considered circuit (Fig. 6) for various values of duty factors D1 and D2 are shown in Figs. 9 and 10. The presented simulation results are shown for phase L1. In the case when the duty factors of MRC1 and MRC2 are equal (D1 = D2 ), it is possible to control only the amplitude of the output Table 1 Circuit parameters. Parameter
Name
Value
Unit
US F nTR1 , nTR2
Supply voltage Supply voltage frequency Transformer voltage ratio TR1, TR2 Input filter inductances of MRC1, MRC2 Inductances of MRC1, MRC2 Capacitance of MRC1, MRC2 Input filter capacitances of MRC1, MRC2 Load impedance Switching frequency – Bidirectional IGBT switches (experiment)
3 × 400/230a 50 1:1
V Hz –
1
mH
1
mH
10
F
10
F
100 5 0.7 IRG4PHUD
kHz s –
LF1 , LF2 L1 , L2 , LL1 , LL2 C1 , C2 , CF1 , CF2
The main specification and components used are shown in Table 1. The presented simulation results were obtained from a simulation environment for power electronics, power conversion and control PSim [27]. ´ The Cuk B2 matrix-reactance chopper is controlled via a simple PWM with a “dead time” control strategy. During simulation tests the “dead time” was set to 0.7 s. The switching frequency is set to 5 kHz. Taking into account the IGBT parameters used this value
CF1 , CF2 ZL1 , ZL2 , ZL3 fS “dead time” S1 ,S2 ,S3 ,S4 a
Experiment—US = 20 V.
J. Kaniewski / Electric Power Systems Research 125 (2015) 203–210
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Fig. 7. Diagrams of voltage phasors in various conditions: (a) D1 = D2 ; US = 0, UL = Ucomp , (b) D1 = / D2 ; UL = US , (c) D1 = D2 ; UL < US , d) D1 = / D2 ; UL < US .
voltage (Fig. 9). The output voltage UL could be higher (Fig. 9a), equal (Fig. 9b) or lower (Fig. 9c) than the source voltage US . If duty factor D1 = / D2 it is possible to control phase and amplitude of output voltage UL (Fig. 10a and b). 4. Experimental test results A three-phase, 1 kVA prototype, intended to correct mains voltage variations (amplitude and phase) has been built and tested in an open-loop control condition. The parameters of experimental set were identical as in simulation analysis (Table 1). The capacitors used to build the experimental set are ICEL metalized polypropylene film capacitors with capacitance 10 F. The bidirectional switches were implemented with two IRG4PHUD IGBTs connected in emitter-to-emitter configuration. Because of the phenomena of interaction between the main and control circuits, caused by scattering of components in the mechanical construction of the experimental setup, a reduced supply voltage was used. The Experimental voltage time waveforms for various values of duty factors D1 and D2 are shown in Figs. 11 and 12. The presented experimental results are shown for phase L1.
The control of phase and amplitude of the output voltage is shown in Fig. 12. As shown in Fig. 11 the output voltage UL could by higher (Fig. 11a), equal (Fig. 11b) or lower (Fig. 11c) than the source voltage US . Moreover the considered circuit is able to change the phase of output voltage UL with constant amplitude of voltage UL . Change of output voltage parameters (phase and amplitude) is continuous. Furthermore control of amplitude and phase of voltage UL could be conducted independently by the independent change of duty factors D1 and D2 . The acquired experimental results validate theoretical and simulation analysis. 5. Comparison to other existing solutions In the literature there can be found many solutions to improve power quality and which are able to control the amplitude and phase angle of the voltage. Most of the existing methods for controlling voltage phase and amplitude include FACTS devices [9], such as the Static Synchronous Compensator (STATCOM) [9,28], Unified Power Flow Controller (UPFC) [29], Unified Power Quality Conditioner (UPQC) [30] and the Dynamic Voltage Restorer (DVR) [11–13]. In most cases these devices use AC/DC/AC converters
Fig. 8. Static characteristics as a function of duty factors D1 and D2 , (a) magnitude of voltage transmittance, (b) phase of voltage transmittance.
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J. Kaniewski / Electric Power Systems Research 125 (2015) 203–210
Fig. 9. Simulation voltage waveforms for pulse duty factor value: (a) D1 = D2 = D = 0.2, US < UL , (b) D1 = D2 = D = 0.5, US = UL , (c) D1 = D2 = D = 0.65, US > UL .
with DC-energy storage (electrolytic capacitors, batteries, etc.). The DC energy storage unit is bulky and the most expensive part of AC/DC/AC converter, and at the same time susceptible to damage. Furthermore, the application of electrolytic capacitors is a major cause of reduced converter lifetime. The presented solution, in comparison to the above alternatives is based on an AC/AC converter without energy storage unit. One well known device to provide voltage support is STATCOM [28]. The main difference between STATCOM and the described solution (Fig. 6) is the principle of operation and grid connection method. STATCOM is shunt connected to the Grid. Shunt connected devices inject current (capacitive or inductive) into the grid at the point of connection. The described voltage regulator is in effect a series compensator (Fig. 6) and injects voltage in series with the line. In the case of shunt connected devices (as STATCOM), the range of voltage control is limited by the permissible load of transmission line to a few percent
of nominal voltage. The main advantage of described converter in comparison to STATCOM is a wider range of voltage control (up to 50% three-phase voltage sag and swell, and single phase voltage interruption). Another well known device to improve voltage parameters is DVR. Conventional DVR is based on an AC/DC/AC converter [11–13]. The DVR can be equipped with DC energy storage – the energy for compensation is taken from the storage unit – or it can operate without energy storage – the energy for compensation is taken from the power grid. Only DVRs with energy storage are capable of compensating voltage interruption. The main advantage in comparison to conventional DVR without an energy storage unit is the possibility to compensate single phase interruption. In the case of voltage sags deeper than 50% of US , a better solution is to use a DVR with an energy storage system. In the literature there are DVR solutions or solutions based on the DVR concept with an AC/AC converter without DC link or DC energy storage unit [7–9].
Fig. 10. Simulation voltage waveforms for pulse duty factor value: (a) D1 = 0.61 and D2 = 0.47, US = UL , (b) D1 = 0.47 and D2 = 0.61, US > UL .
J. Kaniewski / Electric Power Systems Research 125 (2015) 203–210
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Fig. 11. Experimental voltage waveforms for duty factor values: (a) D1 = D2 = D = 0.2, (b) D1 = D2 = D = 0.5, (c) D1 = D2 = D = 0.67.
Fig. 12. Experimental voltage waveforms for duty factor value: (a) D1 = 0.61 and D2 = 0.47, US = UL , (b) D1 = 0.47 and D2 = 0.61, US = UL .
However, these devices operate only in an “in-phase” mode. This means that the voltage phase angle cannot be controlled. In the case of the solution described in [10] it is possible to control simultaneously voltage amplitude and phase. However, to realize these functions another four bidirectional switches in each phase are required.
6. Conclusions This paper has presented a three-phase AC/AC converter for voltage sag/swell compensation and voltage phase angle control. The operation and circuit have been described, and the main characteristics and voltage time waveforms have been shown. The
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J. Kaniewski / Electric Power Systems Research 125 (2015) 203–210
prototype was built for a rated power of 1 kVA. This prototype was operated using a PWM modulation of the IGBTs. The acquired experimental results validate theoretical and simulation analysis. The presented solution operates without an energy storage unit and can be applied to compensate deep voltage sags and swells (up to 50% of US ), even single phase interrupts. The main advantage in comparison to the conventional solution for voltage supporter is the lack of an expensive and bulky energy storage unit. However, this solution might not be inadequate in the case of a voltage sag deeper than 50% of source voltage. Moreover the presented solution allows for the phase shifting of output voltage and in consequence gives the possibility to control power flow in a two source system. In comparison with quadrature phase shifters the phase of the output voltage is controlled independently with amplitude. The next step of the research will be a more detailed analysis of the considered circuit and implementation of a control circuit with closed control loop. Moreover, future investigations will be conducted with active loads (in a dual-sourced system). References [1] Standard EN 50160, Voltage characteristics of public distribution systems, 2002. ´ I. Hiskansen, Effect of load dynamics on power system damping, [2] J. Milanovic, IEEE Trans. Power Syst. 10 (2 (May)) (1995) 1022–1028. [3] Electrotek Concepts Inc., An assessment of distribution system power quality, volume 2: statistical summary report, final report EPRI TR-106294-V2, prepared for Electric Power Research Institute, May 1996. [4] W.E. Brumsickle, R.S. Schneider, G.A. Luckjiff, D.M. Divan, M.F. McGranaghan, Dynamic sag correctors: cost-effective industrial power line conditioning, IEEE Trans. Ind. Appl. 37 (2001) (Jan/Feb). [5] S. Djokic, J. Desment, G. Vanalme, J. Milanovic, K. Stockman, Sensitivity of personal computer to voltage sags and short interruptions, IEEE Trans. Power Deliv. 20 (1 (Jan)) (2005) 375–383. [6] A. Falce, G. Matas and Y. Da Silva, Voltage sag analysis and solution for an industrial plant with embedded induction motors, in Proceedings of the Industrial Applications Conference 2004, vol. 4, pp. 2573–2578. [7] S. Subramanian, M.K. Mishra, Interphase AC-AC topology for sag supporter, IEEE Tran. Power Electron. 25 (2 (Feb)) (2010) 514–518. [8] E. Babaei, F.K. Mohammad, M. Sabahi, Compensation of voltage disturbances in distribution systems using single-phase dynamic voltage restorer, Electr. Power Syst. Res. 80 (2010) 1413–1420. [9] E. Babaei, F.K. Mohammad, Cross-phase voltage sag compensator for three-phase distribution systems, Electr. Power Energy Syst. 51 (2013) 119–126.
[10] S. Jothibasu, M.K. Mishra, An improved direct AC–AC converter for voltage sag mitigation, IEEE Trans. Ind. Electron. 62 (1 (Jan)) (2015) 21–29. [11] J.G. Nielsen, M. Newman, H. Nielsen, F. Blaabjerg, Control and testing of a dynamic voltage restorer (DVR) at medium voltage level, IEEE Trans. Power Electron. 19 (2004) 806–813 (May). [12] P. Kanjiyga, B. Singh, A. Chandra, K. All-Haddad, SRF theory revisited to control self-supported dynamic voltage restorer (DVR) for unbalanced and nonlinear loads, IEEE Trans. Ind. Appl. 49 (5 (Sep/Oct)) (2013) 2330–2340. [13] R. Omar, N.A. Rahim, Voltage unbalanced compensation using dynamic voltage restorer based on supercapacitor, Electr. Power Energy Syst. 43 (2012) 573–581. [14] P.M. Garcia-Vite, F. Mancilla-David, J.M. Ramirez, Per-sequence vectorswitching matrix converter modules for voltage regulation, IEEE Trans. Ind. Electron. 60 (12 (Dec)) (2013) 5411–5421. [15] A. Shabanpour, A. Reza Seifi, A dynamic voltage restorer based on matrix converter with fuzzy controller, Adv. Electr. Electron. Eng. 10 (3 (Sept)) (2012) 143–151. [16] J. Kaniewski, Z. Fedyczak, G. Benysek, AC voltage sag/swell compensator based on three-phase hybrid transformer with buck-boost matrix-reactance chopper, IEEE Trans. Ind. Electron. 61 (8 (Aug)) (2014) 3835–3846. [17] J. Kaniewski, Analysis and Study of Properties of the Hybrid Transformers (Ph.D. dissertation, In Polish), University of Zielona Góra Press, Zielona Góra, 2011. [18] R. Strzelecki, G. Benysek, M. Jarnut, Energy balancing system for end-user customers, Electr. Rev. 84 (2008) 17–19. [19] R. Strzelecki, G. Benysek, M. Jarnut, Power quality conditioners with minimum number of current sensors requirement, Electr. Rev. 84 (2008) 295–298. [20] N.G. Hingorani, L. Gyugyi, Understanding FACTS, IEEE Press, New York, 1999. [21] F. Jiang, S.S. Choi, G. Shrestha, Power system stability enhancement using static phase shifter, IEEE Trans. Power Electron. 12 (1 (Feb)) (1997) 207–214. [22] J. Kaniewski, Z. Fedyczak, Modelling and analysis of a three-phase quadrature phase shifter with a hybrid transformer, Electr. Rev. (11) (2008) 269–274. [23] L.A.C. Lopez, G. Joos, B.-T. Ooi, A PWM quadrature-booster phase shifter for AC power transmission, IEEE Trans. Power Electron. 12 (1 (Jan)) (1997) 138–143. [24] B.K. Jonson, G. Venkataramanan, A hybrid PWM solid state phase shifter using PWM AC converters, IEEE Trans. Power Deliv. 13 (4 (Oct)) (1998) 1316–1321. [25] Z. Fedyczak, Steady state modeling and circuit functions of the bipolar PWM ´ 2003, AC line matrix-reactance choppers, in: Proceedings of the CPE, Gdansk, pp. 206–213. [26] Z. Fedyczak, I. Korotyeyev, Bipolar PWM AC line matrix-reactance choppersthe steady state basic energetic properies, in: Proceedings of the EPE 2003, Toulouse, 2003. [27] http://powersimtech.com—user giude. [28] A. Jain, K. Joshi, A. Behal, N. Mohan, Voltage regulation with STATCOMs: modeling, control and results, IEEE Trans. Power Deliv. 21 (2 (Apr)) (2006) 726–735A. [29] K.K. Sen, E.J. Stacey, UPFC—unified power flow controller: theory, modeling, and applications, IEEE Trans. Power Deliv. 13 (4 (Oct)) (1998) 1453–1460. [30] T. Benslimante, K. Aliouane, B. Chetate, Voltage and current disturbances elimination with reactive power compensation using unified power quality conditioner, in: Proceedings of the SPEEDAM 2009, Taormina, 23–26 May, 2006, pp. 780–784.
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Three-phase AC/AC converter for voltage sag/swell compensator and ´ B2 matrix-reactance chopper phase shifter based on Cuk Jacek Kaniewski ∗ University of Zielona Góra, Institute of Electrical Engineering, Zielona Góra, Poland
a r t i c l e
i n f o
Article history: Received 19 November 2014 Received in revised form 13 March 2015 Accepted 11 April 2015 Available online 25 May 2015 Keywords: Power quality Voltage sag/swell compensator Phase shifter Power flow control Bipolar matrix-reactance chopper AC/AC converter
a b s t r a c t This paper proposes a new topology for an AC/AC converter without DC energy storage to compensate deep voltage sags and swells and to control the output voltage phase shift. The analyzed topology is based ´ on an AC/AC CukB2 bipolar matrix-reactance chopper. The proposed solution is intended to protect sensitive loads and energy flow control in the AC power grid. The main advantage of the proposed solution is the combination of the properties of a series AC voltage compensator and phase shifters without DC energy storage. The presented AC/AC voltage converter is able to compensate single phase voltage interrupts, three-phase up to 50% voltage sags and swells, and change the phase of output voltage simultaneously and independently in relation to the input voltage. The paper presents an operational description, theoretical analysis and the experimental test results from a 1 kVA laboratory model using a PWM control strategy with open feedback loop. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The parameters of electric energy and its quality are very important, especially from the perspective of the end-user and sensitive loads connected to the grid. The parameters of electric energy are well known and described in [1]. Classification of voltage fluctuation depending on size of voltage change is shown in Fig. 1. Dynamic states in a power grid caused by faults, such as rapid load changes, turn-on/turn-off distribution generators, switching effects of renewable energy sources connected to the grid and atmospheric discharges generate undesirable effects for the end-user, such as voltage variations, voltage unbalance, voltage sags/swells (overvoltages), flicker effect or voltage interruption [2]. The analysis of power quality issues [3,4] shows that in about 92% of all power system events there are voltage sags with 40–50% of nominal value, and with a duration from 2 to 30 periods. Only about 4% of sags occur with a duration from 2 s to 10 min. In the case of AC voltage supply changes, both downward and upward, there is a high risk of damage to devices which are sensitive to voltage changes, for example: personal computers, transceiver devices, medical systems or faulty operation of other devices, such as, AC contactors, lighting loads, variable speed drives or industrial computers. In the case of big industrial plants and factories, voltage sags and swells may cause very large financial damages [5,6]. The application of
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AC/AC converters using a Pulse Width Modulation (PWM) control strategy to construct secondary supply sources (voltage sag and swell compensators and voltage regulators) mitigate the unwanted effects of supply [7–17]. The AC/AC converters described in [7] are based on an AC/AC converter and operate without energy storage. However they are capable of compensating voltage sag only up to 50% of US “in-phase” with mode. This means that they cannot change the voltage phase angle. The solutions described in [8,9] provide good dynamic properties but are operated also only in an “in-phase” mode. The circuit described in [10] can control simultaneously voltage amplitude and phase. However, in order to realize these functions another four bidirectional switches in each phase are required. An often encountered circuit for voltage sag/swell compensation is the DVR (Dynamic Voltage Restorer) [11–15]. The conventional topologies of DVR are based on AC/DC/AC converters with DC energy storage. The DC energy storage unit is a part of the DVR which is both the most expensive part and susceptible to damage. The AC voltage compensator described in [16] operates only in an “in-phase” mode and is intended to compensate voltage perturbation such as voltage sags (deeper than 50% of nominal source voltage) and voltage swell (up to 140% of nominal source voltage). In this solution [16] is not capable of changing the phase of the output voltage. Modern AC power systems (smart grids) allow the connection of low power renewable energy sources (photo voltaic panels—PV, wind generators) to low voltage (LV) AC power systems. Renewable energy sources are connected to the grid by power electronic interfaces [17,18]. Voltage fluctuations in AC power systems can be caused by turning on and turning
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Fig. 1. Classification of voltage variation depending on size of change, UN —nominal supply voltage. ´ Fig. 3. Sinle-phase Cuk B2 matrix-reactance chopper.
2. Circuit and operation description off renewable energy sources connected to the grid, due to being dependent on the condition of the source energy (wind, sun, water flow, etc.). Consequently, this may lead to uncontrolled energy flow between the sources in an AC power grid. To eliminate uncontrolled energy flow in the AC power system such devices as phase shifters are used. The phase control of the line voltage in the power grid is one of the well-known methods for power flow control Eq. (1) and for transient stability in flexible AC transmission systems (FACTS) [19–21].
P=
US UL X
sin ,
(1)
where, US —source voltage, UL —load voltage, X—line reactance, ˚—angle of phase shift between US and UL . The classical phase shifter for power flow control in the AC power grid, based on an AC/AC converter is shown in Fig. 2. The various topologies of quadrature-booster phase shifters based on AC/AC converters are described in [22–24]. The main disadvantage of these solutions is that change of voltage amplitude depends on phase shifting (Fig. 2b). Moreover, often the change of the phase of output voltage is possible only in one direction [22–24]. The necessity to control the phase of voltage occurs not only in the case of power flow control Eq. (1) [22,23]. In the case of asymmetrical ungrounded short circuits in the AC power grid, fluctuation of both phase and amplitude of voltage parameters is caused. Having regard to the above, it is reasonable to construct devices with the ability to compensate simultaneously and independently voltage fluctuation and phase control of the AC line voltage. The paper presents a new topology of AC/AC converter destined to mitigate both voltage sags and swells and the phase of voltage fluctuation. Additionally presented is a solution with the ability to compensate single phase voltage interruptions and which operates without a DC energy storage. The described solution is an interesting alternative to conventional AC voltage sag/swell and interrupt compensators with DC energy storage.
´ uk B2 matrix-reactance choppers 2.1. AC/AC converter based on C The topology of the considered circuit of AC voltage sag/swell compensator with phase shifter function is based on the DVR concept. Used as a power electronic converter (in the described ´ solution) is a bipolar matrix-reactance chopper (MRC) Cuk B2 type with bidirectional switches S1 and S2 and input/output filters (Fig. 3). This converter is a direct AC/AC converter and operates without DC energy storage [25,26]. The idealized voltage transmittance understood as a voltage transform function and defined as the ratio of the output voltage value to the input voltage value of the MRC used (Fig. 3) is described by Eq. (2) and shown in Fig. 4a [25,26].
CukB2 U (1 − 2D) ´ H- U = U- 2 ≈ (1 − D) , -1
(2)
where, D—pulse duty factor defined as D = ton /TS , where TS —switching period, ton —turn-on time of switch S1. The idealized characteristic magnitude of voltage and phase of ´ voltage transmittance of Cuk B2 MRC as a function of pulse duty factor D are shown in Fig. 4a and b, respectively. As is shown in Fig. 4a for D < 0.5 the magnitude of voltage trans´ mittance is 1 > HU CukB2 > 0 and output voltage is in phase in relation to input voltage of MRC (Fig. 4b). Within this operational range ´ (D < 0.5, 1 > HU CukB2 > 0) the MRC operates with buck character. The phase of voltage transmittance is changed by for pulse duty factor ´ D > 0.5 (Fig. 4b). For D ≈ 0.67 the output voltage of MRC Cuk B2 (U2 ) is approximately equal to input voltage U1 , but is in the opposite ´ phase in relation to U1 . At operational range (D > 0.67, 1 < HU CukB2 ) ´ the MRC operates with boost character. The MRC Cuk B2 is called ´ a bipolar converter because the output voltage of the MRC Cuk B2 ´ could be changed in phase by . In the real circuit of a MRC Cuk B2 the useful working area is limited. Because of voltage transmittance, the input power factor rapidly decreases for D > 0.75 [16,17] and the useful working area should be limited from D = 0 to D = 0.75 (Fig. 4).
Fig. 2. Classical quadrature-booster phase shifter, (a) schematic, (b) voltage phasors.
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Fig. 4. Idealized chatacteristic as a function of duty cycle D, (a) voltage transmittance, (b) phase of voltage transmittance.
The schematic diagram of the AC/AC converter used is based on ´ two single phase Cuk B2 MRCs and is shown in Fig. 5. The outputs of both MRCs (MRC 1 and MRC 2) are connected to the primary side of the transformers TR1 and TR2 , respectively. The secondary sides of TR1 and TR2 are connected in series (Fig. 5). The voltage ratio of TR1 and TR2 is equal 1 (nTR1 = nTR2 = n = 1). The both of matrix-reactance choppers are controlled via a simple PWM with a “dead time” control strategy (Fig. 5b). The output voltage of the AC/AC converter ´ (ucomp1 ) is the sum of output voltages of the particular Cuk B2 MRCs (uMRC1 , uMRC2 ) including the voltage ratio of the transformers (n)
L2 and L3. The output of AC/AC I converter (U1-U2) is connected in series between source and load (Fig. 6). Connected in an analogous way are the other AC/AC converters in phase L2 and L3. The source line voltages in a three-phase system are described as: Eqs. (3)–(5) j0 U - S1 = US × e ,
(3)
j U - S2 = US × e
−2 3
j U - S3 = US × e
2 3
,
(4)
,
(5)
2.2. Three-phase main circuit A simplified schematic diagram of the proposed voltage compensator for correcting sag/swell and control of voltage phase angle is shown in Fig. 6. As is shown in Fig. 6 the considered circuit contains three units of AC/AC converter (AC/AC I, AC/AC II and AC/AC III). Each module ´ of the AC/AC converter contains two single phase Cuk B2 MRCs in each phase (Fig. 5). The input connectors of the AC/AC converter operate in phase L1 (AC/AC I) are connected to connectors of phase
where, US is the maximum value of the amplitude of the source voltage in three-phase system (Fig. 6). Taking into account the idealized ´ voltage transmittance of the Cuk B2 matrix-reactance chopper Eq. (2), the idealized voltage transmittances of MRC1 and MRC2 are defined as Eqs. (6) and (7).
MRC1 U MRC1 (1 − 2D1 ) H U = , ≈
(6)
MRC2 U MRC2 (1 − 2D2 ) H U = , ≈
(7)
-
U - S2
-
(1 − D1 )
U - S3
(1 − D2 )
where, D1 and D2 —duty factor of MRC1 and MRC2, respectively. The duty factors (D1 and D2 ) of the MRC1 and MRC2 are controlled independently. Taking into account Eqs. (6) and (7) and the voltage ratio of TR1, TR2 (nTR1 = nTR2 = n = 1), the compensating voltage Ucomp1 for line L1 is a sum of output voltages nUMRC1 and nUMRC2 Eq. (8). U - comp1 = n × U - MRC1 + n × U - MRC2 = n×U - S2
(1 − 2D ) 1
(1 − D1 )
+n×U - S3
(1 − 2D ) 2
(1 − D2 )
.
(8)
With regard to the source line voltages Eqs. (3)–(5) the compensating voltage Eq. (8) can be described as Eq. (9):
j U - comp1 = n × US e
−2 3
×
(1 − 2D ) 1
(1 − D1 )
+ ej
2 3
×
(1 − 2D ) 2
(1 − D2 )
, (9)
Because the load voltage (UL ) of the considered circuit (Fig. 6) is a sum of source voltage US and compensating voltage Ucomp , then the load voltage for line L1 can by described as Eq. (10): U - L1 = U - S1 + U - comp1 = US × ej0 + n ´ Fig. 5. AC/AC converter based on two single-phase Cuk B2 MRCs, (a) main circuit, (b) simplify schematic block diagram of used PWM modulator.
× US ej
−2 3
×
(1 − 2D ) 1
(1 − D1 )
+ ej
2 3
×
(1 − 2D ) 2
(1 − D2 )
.
(10)
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Fig. 6. Voltage sag/swell compensator with phase shifter function.
The voltage transmittance of the considered voltage compensator is given by Eq. (11). U - L1 H - U = US -
= ej0 + n × ej
−2 3
×
(1 − 2D ) 1
(1 − D1 )
+ ej
2 3
×
(1 − 2D ) 2
(1 − D2 )
. (11)
The diagrams of the voltage phasors of the considered circuit (Fig. 6), for different values of duty factors D1 and D2 , illustrating the principle of operation, are shown in Fig. 7 As can be seen (Fig. 7) it is possible to obtain an output voltage UL higher (Fig. 7a), lower (Fig. 7c and d), equal to (Fig. 7b), and in phase (Fig. 7a and c) or shifted in phase (Fig. 7b and d) in relation to the source voltage US . Because the voltage Ucomp1 (in line L1) is constructed from line voltages L2 and L3 it is possible to compensate single phase interrupt in line L1 (Fig. 7a). In this case MRC1 and MRC2 are operated with duty factor D1 = D2 = 0 (HU MRC1 = HU MRC2 = 1). Analogously is the case of voltage interrupt in phase L2 or L3. The compensation of voltage interruption is possible just in case single phase interrupts. 3. Simulation test results
(5 kHz) is a sort of compromise between commutation and conducting losses generated by power electronic switches. The resonant frequency (f0 ) of filters is set to about 1/3 of switching frequency (fS ).This condition (f0 = 1/3 fS ) is sufficient to obtain good filtration of higher harmonic components from the switching frequency. The voltage harmonic content (THDU ) is lower than 5%. The Idealized static characteristics of magnitude and phase of voltage transmittance of the considered circuit as a function of duty factors D1 and D2 are shown in Fig. 8. Simulation voltage waveforms in the considered circuit (Fig. 6) for various values of duty factors D1 and D2 are shown in Figs. 9 and 10. The presented simulation results are shown for phase L1. In the case when the duty factors of MRC1 and MRC2 are equal (D1 = D2 ), it is possible to control only the amplitude of the output Table 1 Circuit parameters. Parameter
Name
Value
Unit
US F nTR1 , nTR2
Supply voltage Supply voltage frequency Transformer voltage ratio TR1, TR2 Input filter inductances of MRC1, MRC2 Inductances of MRC1, MRC2 Capacitance of MRC1, MRC2 Input filter capacitances of MRC1, MRC2 Load impedance Switching frequency – Bidirectional IGBT switches (experiment)
3 × 400/230a 50 1:1
V Hz –
1
mH
1
mH
10
F
10
F
100 5 0.7 IRG4PHUD
kHz s –
LF1 , LF2 L1 , L2 , LL1 , LL2 C1 , C2 , CF1 , CF2
The main specification and components used are shown in Table 1. The presented simulation results were obtained from a simulation environment for power electronics, power conversion and control PSim [27]. ´ The Cuk B2 matrix-reactance chopper is controlled via a simple PWM with a “dead time” control strategy. During simulation tests the “dead time” was set to 0.7 s. The switching frequency is set to 5 kHz. Taking into account the IGBT parameters used this value
CF1 , CF2 ZL1 , ZL2 , ZL3 fS “dead time” S1 ,S2 ,S3 ,S4 a
Experiment—US = 20 V.
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Fig. 7. Diagrams of voltage phasors in various conditions: (a) D1 = D2 ; US = 0, UL = Ucomp , (b) D1 = / D2 ; UL = US , (c) D1 = D2 ; UL < US , d) D1 = / D2 ; UL < US .
voltage (Fig. 9). The output voltage UL could be higher (Fig. 9a), equal (Fig. 9b) or lower (Fig. 9c) than the source voltage US . If duty factor D1 = / D2 it is possible to control phase and amplitude of output voltage UL (Fig. 10a and b). 4. Experimental test results A three-phase, 1 kVA prototype, intended to correct mains voltage variations (amplitude and phase) has been built and tested in an open-loop control condition. The parameters of experimental set were identical as in simulation analysis (Table 1). The capacitors used to build the experimental set are ICEL metalized polypropylene film capacitors with capacitance 10 F. The bidirectional switches were implemented with two IRG4PHUD IGBTs connected in emitter-to-emitter configuration. Because of the phenomena of interaction between the main and control circuits, caused by scattering of components in the mechanical construction of the experimental setup, a reduced supply voltage was used. The Experimental voltage time waveforms for various values of duty factors D1 and D2 are shown in Figs. 11 and 12. The presented experimental results are shown for phase L1.
The control of phase and amplitude of the output voltage is shown in Fig. 12. As shown in Fig. 11 the output voltage UL could by higher (Fig. 11a), equal (Fig. 11b) or lower (Fig. 11c) than the source voltage US . Moreover the considered circuit is able to change the phase of output voltage UL with constant amplitude of voltage UL . Change of output voltage parameters (phase and amplitude) is continuous. Furthermore control of amplitude and phase of voltage UL could be conducted independently by the independent change of duty factors D1 and D2 . The acquired experimental results validate theoretical and simulation analysis. 5. Comparison to other existing solutions In the literature there can be found many solutions to improve power quality and which are able to control the amplitude and phase angle of the voltage. Most of the existing methods for controlling voltage phase and amplitude include FACTS devices [9], such as the Static Synchronous Compensator (STATCOM) [9,28], Unified Power Flow Controller (UPFC) [29], Unified Power Quality Conditioner (UPQC) [30] and the Dynamic Voltage Restorer (DVR) [11–13]. In most cases these devices use AC/DC/AC converters
Fig. 8. Static characteristics as a function of duty factors D1 and D2 , (a) magnitude of voltage transmittance, (b) phase of voltage transmittance.
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Fig. 9. Simulation voltage waveforms for pulse duty factor value: (a) D1 = D2 = D = 0.2, US < UL , (b) D1 = D2 = D = 0.5, US = UL , (c) D1 = D2 = D = 0.65, US > UL .
with DC-energy storage (electrolytic capacitors, batteries, etc.). The DC energy storage unit is bulky and the most expensive part of AC/DC/AC converter, and at the same time susceptible to damage. Furthermore, the application of electrolytic capacitors is a major cause of reduced converter lifetime. The presented solution, in comparison to the above alternatives is based on an AC/AC converter without energy storage unit. One well known device to provide voltage support is STATCOM [28]. The main difference between STATCOM and the described solution (Fig. 6) is the principle of operation and grid connection method. STATCOM is shunt connected to the Grid. Shunt connected devices inject current (capacitive or inductive) into the grid at the point of connection. The described voltage regulator is in effect a series compensator (Fig. 6) and injects voltage in series with the line. In the case of shunt connected devices (as STATCOM), the range of voltage control is limited by the permissible load of transmission line to a few percent
of nominal voltage. The main advantage of described converter in comparison to STATCOM is a wider range of voltage control (up to 50% three-phase voltage sag and swell, and single phase voltage interruption). Another well known device to improve voltage parameters is DVR. Conventional DVR is based on an AC/DC/AC converter [11–13]. The DVR can be equipped with DC energy storage – the energy for compensation is taken from the storage unit – or it can operate without energy storage – the energy for compensation is taken from the power grid. Only DVRs with energy storage are capable of compensating voltage interruption. The main advantage in comparison to conventional DVR without an energy storage unit is the possibility to compensate single phase interruption. In the case of voltage sags deeper than 50% of US , a better solution is to use a DVR with an energy storage system. In the literature there are DVR solutions or solutions based on the DVR concept with an AC/AC converter without DC link or DC energy storage unit [7–9].
Fig. 10. Simulation voltage waveforms for pulse duty factor value: (a) D1 = 0.61 and D2 = 0.47, US = UL , (b) D1 = 0.47 and D2 = 0.61, US > UL .
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Fig. 11. Experimental voltage waveforms for duty factor values: (a) D1 = D2 = D = 0.2, (b) D1 = D2 = D = 0.5, (c) D1 = D2 = D = 0.67.
Fig. 12. Experimental voltage waveforms for duty factor value: (a) D1 = 0.61 and D2 = 0.47, US = UL , (b) D1 = 0.47 and D2 = 0.61, US = UL .
However, these devices operate only in an “in-phase” mode. This means that the voltage phase angle cannot be controlled. In the case of the solution described in [10] it is possible to control simultaneously voltage amplitude and phase. However, to realize these functions another four bidirectional switches in each phase are required.
6. Conclusions This paper has presented a three-phase AC/AC converter for voltage sag/swell compensation and voltage phase angle control. The operation and circuit have been described, and the main characteristics and voltage time waveforms have been shown. The
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prototype was built for a rated power of 1 kVA. This prototype was operated using a PWM modulation of the IGBTs. The acquired experimental results validate theoretical and simulation analysis. The presented solution operates without an energy storage unit and can be applied to compensate deep voltage sags and swells (up to 50% of US ), even single phase interrupts. The main advantage in comparison to the conventional solution for voltage supporter is the lack of an expensive and bulky energy storage unit. However, this solution might not be inadequate in the case of a voltage sag deeper than 50% of source voltage. Moreover the presented solution allows for the phase shifting of output voltage and in consequence gives the possibility to control power flow in a two source system. In comparison with quadrature phase shifters the phase of the output voltage is controlled independently with amplitude. The next step of the research will be a more detailed analysis of the considered circuit and implementation of a control circuit with closed control loop. Moreover, future investigations will be conducted with active loads (in a dual-sourced system). References [1] Standard EN 50160, Voltage characteristics of public distribution systems, 2002. ´ I. Hiskansen, Effect of load dynamics on power system damping, [2] J. Milanovic, IEEE Trans. Power Syst. 10 (2 (May)) (1995) 1022–1028. [3] Electrotek Concepts Inc., An assessment of distribution system power quality, volume 2: statistical summary report, final report EPRI TR-106294-V2, prepared for Electric Power Research Institute, May 1996. [4] W.E. Brumsickle, R.S. Schneider, G.A. Luckjiff, D.M. Divan, M.F. McGranaghan, Dynamic sag correctors: cost-effective industrial power line conditioning, IEEE Trans. Ind. Appl. 37 (2001) (Jan/Feb). [5] S. Djokic, J. Desment, G. Vanalme, J. Milanovic, K. Stockman, Sensitivity of personal computer to voltage sags and short interruptions, IEEE Trans. Power Deliv. 20 (1 (Jan)) (2005) 375–383. [6] A. Falce, G. Matas and Y. Da Silva, Voltage sag analysis and solution for an industrial plant with embedded induction motors, in Proceedings of the Industrial Applications Conference 2004, vol. 4, pp. 2573–2578. [7] S. Subramanian, M.K. Mishra, Interphase AC-AC topology for sag supporter, IEEE Tran. Power Electron. 25 (2 (Feb)) (2010) 514–518. [8] E. Babaei, F.K. Mohammad, M. Sabahi, Compensation of voltage disturbances in distribution systems using single-phase dynamic voltage restorer, Electr. Power Syst. Res. 80 (2010) 1413–1420. [9] E. Babaei, F.K. Mohammad, Cross-phase voltage sag compensator for three-phase distribution systems, Electr. Power Energy Syst. 51 (2013) 119–126.
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