Feedback Linearization Control of an H-Bridge Multi Level Inverter

Transcription

1 International Journal of Electronics an Electrical Engineering Vol. 4, No., February 6 Feebac Linearization ontrol of an H-Brige Multi Level Inverter Abir Rehaoulia, Habib Rehaoulia, an Farhat Fnaiech ENSIT/Research Lab SIME, Tunis, Tunisia abirrehaoulia@gmail.com, {habib.rahaoulia, farhat fnaiech}@esstt.rnu.tn Mahir Dursun Faculty of Technology, Department of Electrical an Electronics Engineering, Gazi University, Anara, Turey mursun@gazi.eu.tr Abstract The present paper concerns the control of a multi level inverter in autonomous operation. The inverter is a 5 level H-brige type associate to a suitable L filter. To control the system output voltages, a feebac linearization algorithm is evelope with unnown loa. Simulation is carrie out for either passive or active loas. The ability of the controller to follow perfectly the esire reference was teste on a passive loa. For a loa sensitive to voltage change, lie an inuction motor, the stuy shows that the controller maintains the output voltage to its rate value uner severe conitions. ila r,l i lb 5L H-brige Multilevel Inverter i OA V OA V OB i OB Loa il VO i O Figure. 5L H-brige inverter with L filter an loa. 6 Inex Terms multi level inverter, H-brige, L filter, autonomous operation, feebac linearization 4 I. Van (V) INTRODUTION Multi level inverters appeare in the early eighties. Since, their avantages are well assume [], []. Their particular topologies limit stresses across switches an provie output voltages with reuce harmonic istortion [], [3]. Among the popular multi level inverters, the Hbrige inverter is istinguishe by its simple structure. This latter consists of connecting in series single phase full brige cells. In this stuy, we choose the five-level structure associate to a low pass filter. It allows to profit from previously mentione multi-level benefits without resorting to excessive use of H cells an D sources. The combination of a low pass filter, whose cut-off frequency is well chosen, reuces the total harmonic istortion (THD) of the output voltage to better values than those obtaine by inverters which number of levels is higher than five. In aition, to control the output voltage of the system, we have evelope an algorithm base on feebac linearization techniques. Such control algorithm is stable with very fast response time, compare to conventional controllers. Finally, two useful applications are etaile an reporte. They concern either passive or active loas time (s) Figure. Phase voltage of 5L H-brige multilevel inverter. Uab (V) time (s) Figure 3. Line voltage of 5L H-brige multilevel inverter. II. MATHEMATIAL BAKGROUND The power circuit of the H-brige multi level inverter operating in autonomous moe is epicte in Fig.. Selecting the number of levels an filter components Manuscript receive January 7, 5; revise April 7, 5. 6 Int. J. Electron. Electr. Eng. oi:.878/ijeee

2 International Journal of Electronics an Electrical Engineering Vol. 4, No., February 6 esign is a trae off which epens on the system cost an buliness. The stuy assumes that the parameters of the consiere loa are unnown. The structure of the 5L H-brige inverter is mae by series connection of two briges in each arm. Fig. an Fig. 3 show the line an phase voltages of the consiere inverter without filter. The inverter is going to be controlle by means of input output feebac linearization control in orer to regulate the output filter voltages (V OA, V OB, V O ). The three phase inverter moel regaring the A sie is expresse as follows: U r i l i V U r i l i V U r i l i V A la la OA B lb lb OB l l O where (U A, U B, U ) an (i la, i lb, i l ) are respectively the multilevel inverter output voltages an currents, r an l the filter parameters. The ynamics of loa voltages are obtaine through voltage-current relations across capacitors, so that: V i i V i i V i i OA la OA OB lb OB O l O where (i OA, i OB, i O ) enote loa currents an is the filter capacitor. The overall system state space moel can be transforme in (, q) frame as: III. V o V i o i l V V i i o lq r i i i V U l l l r i i i V U l l l l l lq o lq lq l q INPUT OUTPUT FEEDBAK LINEARIZATION ONTROL This strategy was evelope to simplify non linear control by eliminating non linearities. ontrary to conventional Jacobean linearization, whose iea is base on the linear approximation of ynamics aroun a point, the feebac concept is an exact state transformation in close loop [4]-[7]. Its control principle inclues two steps: To generate a linear input/output relationship by hanling algebraic equations of the state space moel associate to the nonlinear system. () () (3) To esign controller that enables the application of linear control. Since the stuie system is a nonlinear multi input multi output one, its state space moel can be written in matrix form such as: x f ( x) g( x). u (4) Notice that x is the state vector, u the control vector an f(x) an g(x) are vector fiels. They are efine as follows: x Vo x V U x, u x 3 i l U (5) q x 4 i lq x x3 io c c x x4 i c c f ( x), g( x) r x l x3 x 4 l l r x l x3 x 4 l l The main purpose of this paper is to control output filter voltages to fulfill the esire references whatever the loa is. Accoringly, V o an V are the moel outputs an the output vector y is mae up by the first an secon states, equation (7). y x Vo y y x V Applying the input output feebac linearization control, each output is ifferentiate just one time an the control variables appear as in (8), [8], [9]: io y x r x3 x4 i u y x x3 r x4 io i u where is the filter corner frequency. l Hence, the relative egree of the outputs is two. From the above equation, we erive the matrix form of (9): y a u Ex ( ). y a u The ecoupling matrix E(x) is euce so that: Ex ( ) (6) (7) (8) (9) () 6 Int. J. Electron. Electr. Eng. 5

3 International Journal of Electronics an Electrical Engineering Vol. 4, No., February 6 Equation () illustrates the new linear relationship between inputs an outputs. y v y v The bloc iagram of Fig. 4 epicts the H-brige/L filter power circuit an its control scheme using input output feebac linearization. () IV. SIMULATION AND RESULTS () where v an v are the new linear control laws. It can be notice that E(x) is clearly non singular, consequently we can calculate the inverter moulation inex in (, q) frame m an mq via equation (). m Vc mq Vc v x r x3 x4 io i () () v x r x3 x4 i io Finally, to ensure a zero error between the controlle ynamics an their references, the appropriate controller is esigne accoring to equation (3), []. e e e I e eq eq eq I eq A. ase of Passive Loa The effectiveness of the esigne controller is verifie for a passive loa, a resistance in this case. Fig. 5 shows that the filter output voltages are perfectly regulate since they trac their references even if they are change. (3) This is also vali for Vo an V. It can be observe that the ynamics reach rapily their references an present small oscillations, Fig. 6. (VOA, VOB, VO) are poor on harmonics an their waveforms are almost sinusoial. This is illustrate in Fig. 7 which presents a low total harmonic istortion of.8%. Fig. 8 epicts the evolution of component linear control laws use to moulate the multilevel inverter. (3) where e = Vo - Vo, eq = V - V an Vo, V enote the esire reference voltage signals in (, q) frame. Substituting (3) in (3) leas to: v Vo Vo Vo VO VOq - il io I Vo Vo (4) (4) v V V V VO VOq ilq ioq I V V 4 Vo(A,B,) ila H-brige Multilevel Inverter V OB..5 Figure 5. Output filter voltages. Loa AB q PWM.5 5 i O 3 Uq 3 3 Linearizing ontrol Law AB q ilq il V Vo F Fq Vo V Vo 4 UA UB U i OB VO il ma mb m U -4 i OA V OA i lb - where ij are the controller parameters etermine using pole placement metho. r,l We shall test the algorithm evelope on two common cases for voltage control. The first eals with the eliberate variation of the voltage supplying a passive loa, resistor bench for heating, as example. The secon eals with maintaining the voltage to a nominal value, it is the case of an inuction motor, for instance. The parameters of simulate system are: H-brige multilevel inverter: Vc= V, fsw= 5KHz L filter: r=.5ω, L= mh, = µf Resistive loa: R= 3 Ω Inuction motor: pole pairs, Rs=8. Ω, Rr=6.73 Ω, Lm=.9 H, ls=lr=.67 H. All simulations were performe with Matlab Simulin. Feebac linearization ontrol i io V Vo -.5. Figure 4. Input output feebac linearization control of an H-brige multilevel inverter operating in islane moe. 6 Int. J. Electron. Electr. Eng. Figure 6. Vo an V versus time. 6.5

4 International Journal of Electronics an Electrical Engineering Vol. 4, No., February 6 Mag (% of Funamental) Funamental (5Hz) = 35.4, THD=.8% Harmonic orer Figure 7. Harmonic spectrum of loa voltage. phase current (A) Figure. Phase motor current. U (V) Figure 8. Dynamic response of U. phase voltage(v) Figure. Phase motor voltage. B. ase of Active Loa It is well nown that the mechanical torque of an inuction motor is proportional to the square of the supply voltage. A slight voltage rop results in a significant egraation of its torque, hence the necessity to operate at its rate voltage. To this en, we impose the system a constant reference for obtaining a phase voltage of 3V. Then, the inuction motor is starte without loa from the rest, Fig. 9. At time t =.35S, the motor is suenly loae by a loa torque of 4N. Fig. illustrates the relatively high inrush current after inserting the loa torque an especially uring the first moments of starting. Despite the voltage rop cause by the filter elements r an l, the voltage at the motor terminals is maintaine perfectly constant at 3V, Fig.. This emonstrates, once again, the robustness of the control algorithm base on feebac linearization. It is able to fulfill the requirements even in severe moe of operations. Tem(N) Figure 9. Evolution of the motor torque. V. ONLUSION The paper has presente the control of a 5 level H- brige inverter by means of a feebac linearization algorithm. The evelope control algorithm can be applie with any loa without changing the controller esign. The investigation proves the ability an the effectiveness of the selecte algorithm to maintain the output voltage to the esire value uner severe conitions, either for passive or active loas. REFERENES [] M. Malinowsi, K. Gopaumar, J. Roriguez, an M. A. Pérez, A survey on cascae multilevel inverters, IEEE Transactions on Iustrial Electronics, vol. 57, pp. 97-6, Jul.. [] I. ola, et al., Review of multilevel voltage source inverter topologies an control schemes, Energy onversion an Management, vol. 5, no., pp. 4-8, Feb.. [3] P. Veena, et al., Review of gri integration schemes for renewable power generation system, Renewable an Sustainable Energy Reviews, vol. 34, pp , Jun. 4. [4] L. Yacoubi, K. Al Haa, L. A. Dessaint, an F. Fnaiech, A DSP-Base implementation of a nonlinear moel refrence aaptive control for a three-phase NP boost rectifer prototype, IEEE Transactions on Power Electronics, vol., pp. 84-9, Sep. 5. [5] M. Hamoua, K. AL-Haa, F. Fnaiech, an H. Blanchette, Input-State feebac linearization control of two-stage matrix converters interface with high-spee microturbine generators, in Proc. Electrical Power onference, Montreal, Q, anaa, Oct. 7, pp [6] S. obreces, J. Boronau, J. Salaet, E. J. Bueno, an Francisco, an J. Roriguez, Exact linearization nonlinear neutral-point voltage control for single-phase three-level NP converters, IEEE Tansactions on Power Electronics, vol. 4, no., Oct. 9. [7] M. Mehrasa, M. Ahmaigorji, an N. Amjay, A new ual lagrangian moel an input output feeebac linearization control 6 Int. J. Electron. Electr. Eng. 7

5 International Journal of Electronics an Electrical Engineering Vol. 4, No., February 6 of 3-phase/level NP voltage-source rectifier, Automatia, vol. 55, no., pp. 99-, 4. [8]. I. Pop an E. H. Dulf, Robust feebac linearization control for reference tracing an isturbance rejection in nonlinear systems, in Recent Avances in Robust ontrol - Novel Approaches an Design Methos, A. Mueller, E., InTech,, ch., pp [9] H. Zheng an D. Shuai, Nonlinear control of boost converter by state feebac exact linearization, in Proc. 4th hinese ontrol an Decision onference, Taiyuan,, pp [] D. Lalili, A. Mellit, N. Lourci, B. Mejahe, an E. M. Berou, Input output feebac linearization control an variable MPPT algorithm of a gri connecte photovoltaic inverter, Renewable Energy, vol. 36, no., pp , Dec.. Abir Rehaoulia was born in 986 at Tunis, Tunisia. She receive her mathematical baccalaureate in 4, the BSc egree in 8, the MSc egree in an she is woring on the PHD egree since. She is currently an assistant professor at the epartment of Electrical Engineering of ENSIT (Ecole Nationale Supérieure es Ingénieurs e Tunis), University of Tunis, Tunisia. Mrs Abir research interests are Moeling an Simulation of electrical systems, Power Electronics incluing Multi Level Inverters (H-brige, NP, F), Electric Machines an Drives, Avance ontrol Mahir Dursun was born in 97, orum, Turey. He receive the BS egree in 993, the MSc egree in 996, an the PhD egree from Gazi University, Anara, Turey. He is currently an associate professor at the Department of Electric Machinery Eucation, Gazi University. His research interests inclue, Motor Design, Moeling, Motor ontrol, Switche Reluctance Motors, Linear Switche Reluctance Motors, Brushless D motors, D-D converters, Matrix onverters, FL, Artificial Neural Networ, Elevator motors, Motor an entrifugal Pump Drivers, DSP, PL, microprocessors an microcontroller programming, serial an parallel active power filters, an photovoltaic systems, photovoltaic irrigating systems, RF control an communications, an istance eucation material esign. Habib Rehaoulia receive the B.Sc. egree in 978, the M.Sc. egree in 98, the PhD egree in 983, an the habilitation egree in 7, all in Electrical Engineering an from the ENSET (Institute of Technical Sciences), University of Tunis, Tunisia. He joine the teaching staff of the ENSET in 978. Pr Habib Rehaoulia is currently professor at the epartment of Electrical Engineering at ENSIT (National School of Engineers of Tunis), University of Tunis. During his career, he was on leave for several months at WEMPE (University of Maison Wisconsin USA), ENSIEG (University of Grenoble France), Lab. electrotechnique (University of Paris VI France), an the REA (University of Picarie France). His main research interests are Analysis, Moeling an Simulation of electrical machines, Power Electronics, Renewable Energy Farhat Fnaiech was born in 955 in hebba (Tunisia), he receive the BSc egree in Mechanical Engineering in 978 from the ENSET High school of sciences an techniques of Tunis an the master egree in 98, the Doctorate of 3 cycle egree from the same school in Electrical Engineering in 983, an the Doctorate Es Science in Physics from Faculte es Sciences of Tunis in 999. He is currently Professor at the Ecole Nationale Superieure es Ingénieurs e Tunis. Pr Fnaiech has publishe More than 5 research papers in many journals an international conferences. He has organize many national an international conferences an has been the general chairman an member of the international Boar committee of many International onferences, IIT 4, IELIE 6-, ISIE 6-, IEON 5-. He is Associate Eitor of IEEE Transactions Inustrial Electronics. He has serve as IEEE hapter committee coorination sub-committee elegate of Africa Region 8 an Vice hair of IEEE Tunisia Section. He has been appointe as an Aom member in IEEE Inustrial Electronics Society. He is the hea of a big research laboratory in Signal Image an Energy Management in University of Tunis ( researchers). His main interest research areas are nonlinear aaptive Signal processing, nonlinear control of power electronic. 6 Int. J. Electron. Electr. Eng. 8