We are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors

Transcription

1 We are IntechOpen, the worl s leaing publisher of Open Access books Built by scientists, for scientists 3, , M Open access books available International authors an eitors Downloas Our authors are among the 154 ountries elivere to TOP 1% most cite scientists 12.2% ontributors from top 500 universities Selection of our books inexe in the Book itation Inex in Web of Science ore ollection (BKI) Intereste in publishing with us? ontact book.epartment@intechopen.com Numbers isplaye above are base on latest ata collecte. For more information visit

2 Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol Mariya Petkova 1, Mihail Antchev 1 an Vanjo Gourgoulitsov Technical University - Sofia, 2 ollege of Energetics an Electronics - Sofia Bulgaria 1. Introuction The effective operation of the power converters of electrical energy is generally etermine from the chosen operational algorithm of their control system. With the expansion of the application of the Digital Signal Processors in these control systems, graually entering of novel operational principles such as space vector moulation, fuzzy logic, genetic algorithms, etc, is notice. The metho of sliing moe control is applicable in ifferent power electronic converters D/D converters, resonant converters (Sabanovic et al., 1986). The metho application is expane in the quickly eveloping power electronic converters such as active power filters an compensators of the power factor (arenas et al., 1999; Hernanez et al, 1998; Lin et al., 2001; Menalek et al., 2001). In this chart, results of the stuy of a single-phase inverter an single-phase active power filter both with sliing moe control are iscusse. A special feature is the use of control on only one output variable. 2. Single-phase inverter with sliing moe control 2.1 Schematic an operational principle Different methos to generate sinusoial voltage, which supplies ifferent types of consumers, are known. Usually, a version of a square waveform voltage is generate in the inverter output an then using a filter the voltage first orer harmonic is separate. Unipolar or bi-polar pulse-with moulation, selective elimination of harmonics, several level moulation multilevel inverters are applie to improve the harmonic spectrum of the voltage (Antchev, 2009; Mohan, 1994). Inverters with sinusoial output voltage are applicable in the systems of reserve or uninterruptible electrical supply of critical consumers, as well as in the systems for istribute energy generation. In this sub-chart an implementation of sliing moe control of a single-phase inverter using only one variable the inverter output voltage passe to the loa, is stuie. As it is known, two single-phase inverter circuits half-brige an brige, are mainly use in practice (see Fig.1). The inverters are supplie by a D voltage source an a L -filter is connecte in their outputs. The output transformer is require at use of low D voltage, an uner

3 26 Sliing Moe ontrol certain conitions it may be missing in the circuit. The voltage passe to the loa is monitore through a reverse bias using a voltage transucer. The use of a special measuring converter is necessitate by the nee of correct an quick tracing of the changes in the waveform of the loa voltage at the metho use here. In the power electronic converters stuie in the chart, measuring converter V prouce by LEM is applie. a) Fig. 1. a) half-brige an b) brige circuits of an inverter b) Fig.2 isplays a block iagram of the control system of the propose inverter. The control system consists of a generator of reference sinusoi Um sin Θ (it is not shown in the figure), a comparing evice, a comparator with hysteresis an rivers. The control system compares

4 Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol 27 the transitory values of the output voltage of the inverter to these values of the reference sinusoi an epening on the result (negative or positive ifference) control signal is generate. The control signal is passe to the gate of the transistor VT1 or VT2 (for halfbrige circuit) or to the gates of the transistor pairs VT1-VT4 or VT2-VT3 (for brige circuit). Fig. 2. Block iagram of the control system with hysteresis control The process of sliing moe control is illustrate in Fig.3. Seven time moments are iscusse from t 0 to t 6. In the moment t 0 the transistor VT1 of the half-brige schematic, transistors VT1 an VT4 of the brige schematic, respectively, turns on. The voltage of the inverter output capacitor increases fe by the D voltage source. At the reach of the upper hysteresis borerline Um sin Θ + H, where in H is the hysteresis size, at the moment t 1, VT1 turns off (or the pair VT1-VT4 turns off) an VT2 turns on (or the pair VT2-VT3). The voltage of the capacitor starts to ecrease till the moment t 2, when it is equal to the lower hysteresis borerline Um sin Θ H. At this moment the control system switches over the transistors, etc. Therefore the moments t 0, t 2,, t 4 an moments t 1, t 3, t 5 are ientical. Fig. 3. Explanation of the sliing- moe control

5 28 Sliing Moe ontrol 2.2 Mathematical escription Fig.4 isplays the circuit use to make the analysis of sliing moe control of the inverter. The power evices are assume to be ieal an when they are switche over the supply voltage U with altering polarity is passe to the L -filter. L + ( ) i L U (+) i i Fig. 4. ircuit use to make the analysis of sliing moe control of the inverter The loa current an the current of the output transformer, if it is connecte in the schematic, is marke as i L. From the operational principle, it is obvious that one output variable is monitore the voltage of the capacitor u. Its transient value is change through appling the voltage U with an altering sign. The task (the moel) is: u = U ωt (1) REF M.sin As a control variable, the prouction uu. may be examine, where in: u= sgn[( u u ) H] REF u= + 1 when( u u ) < H u= 1 when( u u ) > H REF REF (2) The following relationships are vali for the circuit shown in Fig.4: U = u + L t i = i + i i L u = t i (3) Using (3) an after several transformations, it is foun: u 1 1 il u = = U. t ut t L. L (4) In conformity with the theory of sliing moe control, the following equations are written (Ewars & Spurgeon, 1998): x = u x = u x = u REF (5)

6 Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol 29 The control variable u eq corresponing to the so-calle equivalent control may be foun using the following equation (Utkin, 1977): s = x x = 0 (6) Using (1) an (4) an taking in consieration (5) an (6), it is foun: il 2 ueq = uu. = u + L. L.. ω. UM.sin ω. t (7) t The value foun may be consiere as an average value when the switching is between the maximum U MAX an minimum U MIN values of the control variable (Utkin, 1977; Utkin, 1992). If they coul change between + an, in theory, there is always the probability to achieve a moe of the sliing moe control in a certain range of a change of the output variable. In orer to be such a moe, the following inequalities have to be fulfille: UMIN < ueq < UMAX (8) for physically possible maximum an minimum values. In this case they are: U U MIN MAX = U = + U (9) Resolving (7) in respect to the variable, which is being monitore u, an substituting in (9), the bounary values of the existence of the sliing moe control coul be foun: il 2 u =± U L + L. ω. UM.sinωt (10) t The equation (10) may be interprete as follows: a special feature of the sliing moe control with one output variable the capacitor voltage, is the influence of the loa current changes upon the sliing moe, namely, at a sharp current change it is possible to break the sliing moe control within a certain interval. From this point of view, it is more suitable to operate with a small inuctance value. As the loa voltage has to alter regaring a sinusoi law, let (10) to be analyze aroun the maximum values of the sinusoi waveform. It is foun: i u = ± U L + L... U ( ± 1) L 2 ω M t t= π 2. ω (11) Where in (11) the positive sign is for the positive half perio an the negative one for the negative half perio. After taking in consieration the practically use values of L an (scores microhenrys an microfaras), the frequency of the supply source voltage ( f 50 or 60Hz) = an its maximum value U M ( 325 or 156 V), it is obvious that the influence of the last term coul be neglecte. Thus the maximum values of the sinusoial voltage of the loa are mainly limite from the value of the supply voltage U an the spee of a change of the loa current. So, from the point of view of the sliing moe control,

7 30 Sliing Moe ontrol it is goo the value of U to be chosen bigger. Of course, the value is limite an has to be consiere with the properties of the power switches implemente in the circuit. 2.3 Stuy through computer simulation Stuy of the inverter operation is mae using an appropriate moel for a computer simulation. Software Ora 10.5 is use to fulfill the computer simulation. Fig.5 isplays the schema of the computer simulation. The inverter operation is simulate with the following loas active, active-inuctive (with two values of the inuctance smaller an bigger ones) an with a consierably non-linear loa (single-phase brige uncontrollable rectifier with active-capacitive loa). Only the loa is change uring the simulations. The supply voltage of the inverter U is 250V, = 120 μf an L = 10 μh. Fig. 5. Schematic for the computer simulation stuy of sliing moe control of the inverter The simulation results are given in Fig.6, Fig.7, Fig.8 an Fig.9. The figures isplay the waveform of the voltage feeing the loa, an the loa current, which is isplaye multiplie by 100 for the first three cases an by 40 for the last one.

8 Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol 31 Fig. 6. omputer simulation results of the inverter operation with an active loa equal to 500Ω using sliing moe control. urve 1 the voltage feeing the loa, curve 2 the loa current Fig. 7. omputer simulation results of the inverter operation with an active-inuctive loa equal to 400Ω/840μН using sliing moe control. urve 1 the voltage feeing the loa, curve 2 the loa current Fig. 8. omputer simulation results of the inverter operation with an active-inuctive loa equal to 400Ω/2Н using sliing moe control. urve 1 the voltage feeing the loa, curve 2 the loa current

9 32 Sliing Moe ontrol Fig. 9. omputer simulation results of the inverter operation with single-phase brige uncontrolle rectifier loa using sliing moe control. urve 1 the voltage feeing the loa, curve 2 the loa current The results support the probability using sliing moe control on one variable the output voltage, in the inverter, to obtain a waveform close to sinusoial one of the inverter output voltage feeing ifferent types of loa. 2.4 Experimental stuy Base on the above-mae stuy, single-phase inverter with output power of 600VA is materialize. The brige schematic of the inverter is realize using IRFP450 transistors an transformless connection to the loa. The value of the supply voltage of the inverter is 360V. Fig.10, Fig.11, Fig.12 an Fig.13 isplay the loa voltage an loa current waveforms for the loa cases stuie through the computer simulation. Fig. 10. The loa voltage an loa current in the case of active loa

10 Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol 33 Fig. 11. The loa voltage an loa current in the case of active-inuctive loa with the smaller inuctance Fig. 12. The loa voltage an loa current in the case of active-inuctive loa with the bigger inuctance

11 34 Sliing Moe ontrol Fig. 13. The loa voltage an loa current in the case of single-phase brige rectifier All results show non-sinusoial part of the output voltage less then 1.5% as well as high accuracy of the voltage value (230V ± 2%). 3. Single-phase series active power filter with sliing moe control 3.1 Schematic an operational principle Active power filters are effective means to improve the energy efficiency with respect to an A energy source as well as to improve energy quality (Akagi, 2006). Series active power filters are use to eliminate isturbances in the waveform of a network source voltage in such a way that they compliment the voltage waveform to sinusoial voltage regaring the loa. Usually pulse-with moulation is use to control the filters, but also researches of sliing moe control of the filters on several variables are known (arenas et al, 1999; Hernanez et al, 1998). In this sub-chart sliing moe control of a single-phase series active power filter on one variable the supply voltage of the loa is stuie (Antchev et al, 2007; Antchev et al, 2008). Fig.14 shows the power schematic of the active power filter with the block iagram of its control system. Synchronize to the source network an filtering its voltage, the first orer harmonic of the source voltage is extracte. This harmonic is use as a reference signal U ref. This signal is compare with a certain hysteresis to the transient value of the loa voltage U real. Depening on the sign of the comparison, the appropriate pair of iagonally connecte transistors (VT1-VT4 or VT2-VT3 ) of the inverter is switche on.

12 Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol 35 Fig. 14. Series active power filter with sliing moe control with hysteresis 3.2 Mathematical escription Fig.15 isplays the circuit use to make the analysis of sliing moe control of the converter. The power switches are assume to be ieal an in their switching the source voltage U with an altering polarity is passe to the L -filter. i L u i L us i ul L i U + + ( ) Fig. 15. ircuit use to make the analysis of sliing moe control of the series active power filter ( )

13 36 Sliing Moe ontrol The analysis is similar to those mae for the single-phase inverter. The loa current is marke as i L. From the operational principle, it is clear that one output variable the loa voltage u L is monitore. Its transient value is change through appling the voltage U with an altering sign. The task (the moel) is: u = U ωt (12) REF M.sin As a control variable, the prouction uu. may be examine, where in: ( ) ( L REF) ( ) u= sgn ul uref H u= + 1 when u u < H u= 1 when u u > H L REF (13) The following relationships are vali for the schematic shown in Fig.15: U = u + L t i = i + i С L u i = t u + u = u S L i (14) Using (14), it is foun: ul 1 1 il u L = = us U. t ut t + + L. L (15) In conformity with the theory of sliing moe control, the following equation is written (Ewars & Spurgeon, 1998): x = u x = u x = u L L REF (16) The control variable u eq corresponing to the so-calle equivalent control may be foun using the following equation (Utkin, 1977, Utkin, 1992): s = x x = 0 (17) Using (12) an (15) an taking in consieration (16) an (17), it is foun: il 2 ueq = u. U = ul us Lu S L L.. ω. UM.sin ω. t (18) t The value foun may be consiere as an average value when the switching is between the maximum U MAX an minimum U MIN values of the control variable (Utkin, 1977; Utkin 1978). If they coul change between + an, in theory, there is always the probability

14 Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol 37 to achieve a moe of the sliing moe control in a certain range of a change of the output variable. In orer to be such a moe, the following inequalities have to be fulfille: UMIN < ueq < UMAX (19) for physically possible maximum an minimum values. In this case they are: U U MIN MAX = U = + U (20) Resolving (18) with respect to the variable, which is being monitore u L, an substituting in (20), the bounary values of the existence of the sliing moe control coul be foun: il 2 ul =± U + us + L. + L.. u S + L.. ω. UM.sinωt (21) t The equation (21) foun coul be interprete in the following way: a special feature of the sliing moe control with one output variable the loa voltage, is the influence of the loa current changes upon the sliing moe, namely, at a sharp current change it is possible to break the sliing moe control within a certain interval leaing to istortion in the transient value of the voltage feeing the loa. It is worthy to be mentione that, for example, rectifiers with active-inuctive loa consume current with sharp changes in its transient value from the source. From this point of view, to reuce this influence it is more suitable to operate with a small inuctance value. As the loa voltage has to change regaring a sinusoi law, let (21) to be analyze aroun the maximum values of the sinusoi waveform. It is foun: i u =± U + u + L + L u + L U ± (22) L ( )..( ).. 2..( 1) L S t π S t π ω = M 2. ω t = t= π 2. ω 2. ω Where in (22) the positive sign is for the positive half perio an the negative one for the negative half perio. After taking in consieration the practically use values of L an (scores microhenrys an microfaras), the frequency of the supply source voltage ( f = 50 or 60Hz) an its maximum value U M ( 311 or 156 V), it is obvious that the influence of the last two terms coul be neglecte. Thus the maximum values of the sinusoial voltage of the loa is mainly limite from the value of the supply voltage U, the transient value of the loa voltage an the spee of a change of the loa current. So, from the point of view of the sliing moe control, it is goo the value of U to be chosen bigger. oncerning the conclusion of the influence of the loa current change mae base on the equations (21) an (22), the following may be commente: let us assume the worst case short circuit of the loa terminals (for example uring break own regime or commutation processes in the loa). Then the spee of the current change will be of maximum value an it will be limite only by the impeance of the A supply source in a case of transformless active power filter. When an output transformer is present, its inuctance will be summe to this of the source an it will aitionally ecrease the spee. Taking in consieration the maximum value of the voltage of single-phase network at a low voltage, as well as the range

15 38 Sliing Moe ontrol of the inuctance possible values, the spees tentatively of 1 A orer may be expecte. μs The value of the filter inuctance is within the range of 1 to 3mH. Therefore, the influence of the thir term in equations (21) an (22) will be approximately 10 times lower then the influence of the supply voltage U. 3.3 Stuy through computer simulation In this part, software PSIM is use to stuy single-phase active power filter. The operation of the single-phase active power filter is stuie at a trapezoial waveform of the voltage of the supply source. The computer simulation schematic is shown in Fig.16. The results from the simulation are shown in Fig.17. Total harmonic istortion of the source voltage is assume to be 20%. The altitue of the trapezium is given equal to 300V. The values of the elements in the output of the single-phase uncontrolle rectifier are 1200 μf и 50 Ω. At so chosen waveform of the A source, the results put show goo reaction of APF an also show its effective operation. So chosen trapezium form of the voltage is very close to the real cases of istortion of the source voltage. As it is seen from the results inclue, in this case of the source voltage waveform the system voltage supplying the loa is obtaine to be very close to the ieal sinusoial waveform without istortions aroun the maximum value of the sine wave an without presence of over voltages. Fig. 16. Simulation schematic of operation of the single-phase APF with single-phase uncontrolle rectifier with active-capacitive loa

16 Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol 39 Fig. 17. Results of the simulation of the schematic shown in Fig.16. The upper waveform is the source voltage, the mile one APF voltage, an the lower waveform the voltage passe to the loa 3.4 Experimental stuy A precise stabilizer-filter for single-phase A voltage for loas with power upto 3kVA is materialize. The evice is realize using the block iagram shown in Fig.18. The source voltage U c for the active power filter is provie from a bi-irectional converter connecte to the network. Fig.19 shows the general appearance of the precise stabilizer-filter. Its basic blocks are marke. U S U F U L LOAD I L Biirectional A/ D onverter Uc SERIES ATIVE POWER FILTER L ONTROLSYSTEM OF TheBiiretional A / D onverter ONTROL SYSTEM OF The Active Power Filter Fig. 18. Block iagram of a precise stabilizer-filter of A voltage

17 40 Sliing Moe ontrol Fig. 19. Single-phase precise stabilizer-filter of A voltage Fig. 20. Parameters of the loa voltage when stabilizer APF is switche off

18 Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol 41 Fig.20 isplays the parameters of the loa voltage its value, harmonic spectrum, total harmonic istortion, when the stabilizer APF is switche off. Fig.21 isplays the same results when the stabilizer APF is switche on. Fig.20 shows ecrease effective value of the voltage with 13%, increase fifth harmonic an total harmonic istortion 4.5%. Fig.21 shows the stabilization of the effective value of the loa voltage to (230V - 1.2%), ecrease of the values of all harmonics, as well as a ecrease in the total harmonic istortion to 1.6%. Fig.22 isplays results when the stabilizer APF is switche off, the effective value of the source voltage is increase with approximately 10% an the total harmonic istortion of 3.2%. Fig.23 isplays results when the stabilizer APF is switche on. It is seen a stabilization of the voltage feeing the loa to (230V +1.8%), ecrease of the values of all harmonics, as well as a ecrease in the total harmonic istortion to 1.8%. Fig. 21. Parameters of the loa voltage when stabilizer APF is switche on Fig.24 shows transient processes at a sharp change of the source voltage. The reason that the sinusoial waveform of the voltage is not seen is that the scale of the X-axis is 1s/iv. The aim of this presentation is to be more clear that the value of the voltage feeing the loa o not change significantly at a sharp change of the source voltage (both when its value ecreases or increases) when the precise stabilizer-filter is switche on.

19 42 Sliing Moe ontrol Fig. 22. Parameters of the loa voltage when stabilizer APF is switche off

20 Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol 43 Fig. 23. Parameters of the loa voltage when stabilizer APF is switche on а Fig. 24. Experimental results at a sharp change of the value of the source voltage. a) without APF, b) with APF. The upper oscillograms present the source voltage, the lower ones the loa voltage. b

21 44 Sliing Moe ontrol 4. onclusion The inclue results in the chart prove the effective operation of the single-phase inverter an single-phase active power filter stuie with sliing moe control on one output variable the voltage feeing the loa. The results foun concerning the sliing moe control of inverters an series active power filters base on only one variable may be expane an put into practice for three-phase inverters an three-phase series active power filters. 5. References Akagi H. (2006). Moern active filters an traitional passive filters. Bulletin of the Polish Acaemy of Sciences, Technical Sciences, vol. 54, No 3, Antchev, M.H., Petkova, M.P. & Gurgulitsov, V.T. (2007).Sliing moe control of a series active power filter, IEEE conf. EUROON 2007, Proc., pp , Warshaw, Polan. Antchev, M.H., Gurgulitsov, V.T. & Petkova,,M.P.(2008). Stuy of PWM an sliing moe controls implie to series active power filters, conf. ELMAR 2008, Zaar, hroatia, 2008, pp Antchev, M. (2009). Technologies for Electrical Power onversion, Efficiency an Distribution, Methos an Processes, IGI Global, USA. arenas V.M., Nunez,. & Vazquez, N. (1999). Analysis an Evaluation of ontrol Techniques for Active Power Filters: Sliing Moe ontrol an Proportional- Integral ontrol, Proceeings of APE 99, vol.1, pp Ewars h. & Spurgeon, S. (1998). Sliing moe control theory an applications, Taylor an Francis Hernanez,., Varquez, N. & arenas, V. (1998). Sliing Moe ontrol for A Single Phase Active Power Filter, Power Electronics ongress, 1998 IEP 98. VI IEEE International, pp Lin, B.-R., Tsay, S.-. & Liao, M.-S. (2001). Integrate power factor compensator base on sliing moe controller, Electric Power Applications, IEE Proceeings, Vol. 148, No 3, May Menalek, N., Fnaiech, F. & Dessaint, L.A. (2001). Sliing Moe ontrol of 3-Phase 3-Wire Shunt Active Filter in the q Frame, Proceeings of anaian onf. Electrical an omputer Engineering, vol.2. pp , 2001, anaa Mohan R. (1994). Power Electronics: onverters, Applications an Design, John Wiley an Sons. Sabanovic, A., Sabanovic, N. & Music, O. (1986) Sliing Moe ontrol Of D-A onverters, IEEE 1986, Energoinvest Institute for ontrol an omputer Science Sarajevo, Yugoslavia, pp Utkin V.I. (1977). Variable structure system with sliing moes. IEEE Trans. On A.., Vol.A-22, April 1977, pp Utkin V.I.(1978). Sliing Moes an Their Application in Variable Structure Systems, Moskow, Mir. Utkin V.I.(1992). Sliing Moes in ontrol an Optimization, Springer Ferlag, Berlin. ISBN

22 Sliing Moe ontrol Eite by Prof. Anrzej Bartoszewicz ISBN Har cover, 544 pages Publisher InTech Publishe online 11, April, 2011 Publishe in print eition April, 2011 The main objective of this monograph is to present a broa range of well worke out, recent application stuies as well as theoretical contributions in the fiel of sliing moe control system analysis an esign. The contributions presente here inclue new theoretical evelopments as well as successful applications of variable structure controllers primarily in the fiel of power electronics, electric rives an motion steering systems. They enrich the current state of the art, an motivate an encourage new ieas an solutions in the sliing moe control area. How to reference In orer to correctly reference this scholarly work, feel free to copy an paste the following: Mariya Petkova, Mihail Antchev an Vanjo Gourgoulitsov (2011). Investigation of Single-Phase Inverter an Single-Phase Series Active Power Filter with Sliing Moe ontrol, Sliing Moe ontrol, Prof. Anrzej Bartoszewicz (E.), ISBN: , InTech, Available from: InTech Europe University ampus STeP Ri Slavka Krautzeka 83/A Rijeka, roatia Phone: +385 (51) Fax: +385 (51) InTech hina Unit 405, Office Block, Hotel Equatorial Shanghai No.65, Yan An Roa (West), Shanghai, , hina Phone: Fax:

23 2011 The Author(s). Licensee IntechOpen. This chapter is istribute uner the terms of the reative ommons Attribution-Nonommercial- ShareAlike-3.0 License, which permits use, istribution an reprouction for non-commercial purposes, provie the original is properly cite an erivative works builing on this content are istribute uner the same license.