A DIRECT CONTROL METHOD FOR MULTICELLULAR CONVERTERS

Transcription

1 U.P.B. Sci. Bull., Series C, Vol. 74, Iss. 3, 202 ISSN x A DIRECT CONTROL METHOD FOR MULTICELLULAR CONVERTERS Bogdan Cristian FLOREA, Dan Alexandru STOICHESCU 2, Alexandru SPĂTARU 3 În această lucrare este rezentată o metoda de control directă a convertoarelor multicelulare cc-cc serie. Aceste structuri au câştigat oularitate în erioada recentă datorită avantajelor oferite, şi anume: modularitate, reducerea constrângerilor entru comonente, eficienţă crescută. Pentru a evidenţia erformanţele controlului rous, acesta va fi comarat cu un control de ti PWM. Rezultatele evidenţiază îmbunătăţirile aduse de metoda rousă faţă de una din metodele clasice de comandă a acestor toologii de convertoare. In this aer, a direct control method for dc-dc series multicellular converters is introduced. Multicellular toologies have gained a lot of oularity because of their advantages over classical energy conversion structures. These advantages include: modularity, reduction of comonent constraints, high efficiency. In order to highlight the erformance of the roosed method, it is comared to a PWM control. The results show the imrovements of the roosed method comared to a classic control algorithm for these tye of energy conversion toologies. Keywords: multicellular converter, twisting, control, high order sliding mode. Introduction Energy conversion has always resented interest for researchers, because of the many alications in which energy conversion systems are used. The efficiency of energy conversion has always been the main goal for the research. In high ower alications in articular, the efficiency in the case of classical toologies is very low comared to the same toologies working in low ower alications. The low efficiency is due to the high switching times of high ower comonents. The idea of multicellular converters (fig. ) first aeared in the 990s [], and it roosed a series of elementary commutation cells, linked with floating PhD student., Faculty of Electronics, Telecommunications and Information Technology, University POLITEHNICA of Bucharest, Romania, bogdan.florea@ub.ro 2 Prof., Faculty of Electronics, Telecommunications and Information Technology, University POLITEHNICA of Bucharest, Romania, stoich@elia.ub.ro 3 Prof., Faculty of Electronics, Telecommunications and Information Technology, University POLITEHNICA of Bucharest, Romania

2 58 Bogdan Cristian Florea, Dan Alexandru Stoichescu, Alexandru Sătaru voltage sources. This allowed the distribution of high voltages over more switching elements and, as a consequence, the ability to use switching comonents with lower constraints and better erformances. Fig.. Multicellular converter with cells The floating voltage sources that link the switching cells are actually floating caacitors. The voltage dro across them needs to be regulated by the control algorithm. The comlexity of the control is high because has to maintain the desired outut voltage, while at the same time balance the caacitor voltages around the reference value. Many control algorithms are roosed in literature, for examle: a assivity based control [2], sliding mode control [3], PWM control [4]. The goal of this aer is to introduce an efficient control which imroves the outut error of the classical PWM control. The roosed control is based on a second order sliding mode algorithm which will be resented in section Multicellular converter model The idea of the multicellular converter is that it distributes the high voltage over more switching elements. In order to avoid unbalanced usage of comonents, the voltage is distributed equally across each cell. That means that the voltage dro on each cell is equal to a fraction of the inut voltage E, where is the number of cells (fig. ). In order to ensure that, we must determine the floating caacitor voltages: E VCell = V, k C V k Ck = k = () where VC = 0, V 0 C = E. From equation (), for k =, we have:

3 A direct control method for multicellular converters 59 E E VCell = V C V C = V 0 C = (2) Increasing k, we find the general exression for the caacitor voltages: ke VC k = (3) In order to determine the converter model, we consider two adjacent cells: Cell k and Cell k+ connected with the caacitor C k (fig. 2). Fig. 2. Multicellular converter with cells and an RL load The caacitor voltage VC k is determined by the evolution of the caacitor current. This, in turn, is given by the configuration of the switches: ic = ( s ) k k+ sk io (4) where: s k = if the uer switch in cell k is conducting and s k = 0 if the lower switch in cell k is conducting [5]. The caacitor voltage is then given by (5): dvc dv k Ck ( sk sk) ic = C k k = + io (5) dt dt Ck Equation (5) can be generalized for all caacitors. Next we determine the outut voltage as the sum of all cell voltages (6): VO = VCell = ( ) k VC V k C s k k (6) k= k= From equation (6), we note that we can have multile voltage levels at the outut, deending on the configuration of the switches. For a converter with E 2 E ( ) E cells, we have + voltage levels: 0,,,...,, E [5]. This means that the voltage jums at the outut are smaller than the ones in classical structures. For the multicellular converter with an RL load in fig. 2, the outut current io is given by:

4 60 Bogdan Cristian Florea, Dan Alexandru Stoichescu, Alexandru Sătaru dio VO R = io (7) dt L L From equations (5), (6) and (7) we get the instantaneous model of the multicellular converter in fig. 2: s2 s V C = i O C s3 s V 2 C = i 2 O C2 (8) s s V C = i O C ( s ( s2) ( s2 s3) s s) s R i O = VC + V C + + V 2 C + E i O L L L L L For the remainder of this aer, we will use a 3 cell converter ( = 3) connected to an RL load. 3. Control method The controller needs to accomlish two tasks: rovide the required outut voltage and balance the caacitor voltages around the reference values. Many tyes of controllers exist in literature. One very oular tye of control is the sliding mode control. It has been around for a very long time and it has been thoroughly researched. The disadvantage of using this tye of control is the existence of chattering: high frequency oscillations around the sliding surface. Some solutions have been roosed, like relacing the sign function of the sliding mode with a smoother function in the vicinity of the origin. However, this solution leads to the loss of accuracy and robustness of the system [6]. Another solution is to use higher order sliding modes. They act on the controlled value, as well as on its high order time derivatives. This way, the chattering is reduced significantly and the robustness is reserved. An r th order sliding mode is determined by: r s = s = s = = s = 0 (9) where s is the sliding surface. The roosed control method is based on the twisting algorithm, which is a second order sliding mode. The hase trajectory of the twisting algorithm is shown in figure 3.

5 A direct control method for multicellular converters 6 Fig. 3. Phase trajectory of the twisting algorithm The control law for the algorithm is given by: u, u > ut () = Vm signs (), ss 0, u (0) VM sign(), s ss > 0, u 4Γ where:, M φ VM > Vm Vm >, Vm >, ΓmVM φ >Γ MVm + φ. s0 Γm The twisting algorithm is resonsible for choosing the required outut voltage in order to drive the system along the hase trajectory. The second art of the control is to choose to correct switching combination, so that the required voltage is ensured and the floating caacitor voltages are regulated. In order to determine what the next switching combination is, we must analyze the effect of combination on the caacitor voltages and on the outut. 3 There are 2 = 2 = 8 oerating modes. The oerating modes of the 3 cells converter are resented in table. Table Oerating modes of the multicellular converter V s s 2 s C V C2 3 io 0 i O <0 i O 0 i O <0 V O V C2 + V C2 - E/3 0 0 V C + V C - V C2 - V C2 + E/3 0 V C + V C E/3 0 0 V C - V C E/3 0 V C - V C + V C2 + V C2-2E/ V C2 - V C2 + 2E/ E

6 62 Bogdan Cristian Florea, Dan Alexandru Stoichescu, Alexandru Sătaru We can see that for all voltage levels different from 0 or E, we have redundancy. Also, for those voltage levels, the caacitor voltages are changed. This redundancy allows us to choose the best combination so that we can have the outut voltage required and, at the same time, balance the floating caacitor voltages. Another consequence of having redundancy is that we can otimize the control in order to rolong the life of the switching elements. This is achieved by rioritizing the caacitor voltages that need to be balanced and choosing a combination which requires a minimum number of commutations from the current oerating mode. In order to do this, we must first comute all ossible future modes F M of oeration from the current state sc for the required outut voltage: s s 2 s s s 2 2 s 2 2 FM = () s s i 2 s i i sc = s s2 s The next ste is to determine the number of commutations N S from the current state s c to all the ossible future states: NS = [ m m2 mi] (2) mk = uc( j) FM( k, j), k = i j= The combination with the minimum number of switches mk is chosen. 4. Results The roosed controller was tested in MATLAB/Simulink simulation with the following conditions: E = 300V, C = C 2 = 33μF, L = 0.5mH, R = 0Ω, f = 0kHz In order to test the erformance of the control, it was comared with a PWM control. The PWM control for multicellular choers has the advantage of ensuring a natural balance of the caacitor voltages [7], but the steady state error is considerably higher than the roosed control method. In figures 4 and 5 we see the outut current for the 2 control methods. The reference is 2.5A for both cases. We clearly see that the oscillations for the PWM method is higher than for the direct control roosed in this aer. Also, the

7 A direct control method for multicellular converters 63 overshot at start-u in the case of PWM control is very high and otentially dangerous for the load. Fig. 4. Outut current for PWM control Fig. 5. Outut current for direct control The caacitor voltages are balanced in both cases (figures 6, 7, 8 and 9), but again, in the case of PWM control, the initial overshot is significant, and it is the cause for the current overshot. In the roosed direct control, the overshot is close to zero and the caacitor voltages are maintained balanced. Fig. 6. V C for PWM control Fig. 7. V C2 for PWM control Fig. 8. V C for direct control Fig. 9. V C2 for direct control A comarison between the two methods is resented in table 2.

8 64 Bogdan Cristian Florea, Dan Alexandru Stoichescu, Alexandru Sătaru Comarison between the roosed method and PWM control PWM control Direct control V Cmax (V Cref = 00V) 42.6V 9.3V V C2max (V C2ref = 200V) 57.2V 0.7V t tran 32ms 2ms Table 2 As it is shown in table 2, the maximum deviation for the caacitor voltages in the case of PWM control is very high, esecially during the transient time (figures 6 and 7). This can be dangerous for the circuit and the load and additional circuits are needed in order to have a safe oeration. The roosed method has a much lower maximum variation of caacitor voltages, even during transient time, variation which is contained in the ±0% interval which we allowed for the floating voltages. One can also see the reduction of transient time for the roosed method, which rovides a better resonse for the circuit. 5. Conclusions The roosed method works with good results, which was highlighted in comarison with the classic PWM control. The results show that for the same configuration, the results are imroved about 0 times, and at the same time, the dangerous overshot is eliminated. In order to rotect the load in the case of PWM control, a start-u routine is necessary, whereas in the case of the roosed direct control, this ste is eliminated, thus making the system more resonsive. This is shown also in terms of the transient time for the system, which is greatly imroved in the roosed method. R E F E R E N C E S [] Th. Meynard, H. Foch, Disositif de conversion d energie electrique a semiconducteur, brevet francais no. 9,09582, Euroe, Jaan, USA, Canada, 92,00652 [2] H. Sira-Ramirez, R.P. Moreno, R. Ortega, M.G. Esteban Passivity-based controllers for the stabilization of dc-t-dc ower converters, Automatica, 33, ag , 997 [3] L.Amet, M. Ghanes, J.P. Barbot, Direct control based on sliding mode techniques for multicell serial choer, American Control Conference 20, ag , 20 [4] G. Gateau, M. Fadel, P. Maussion, R. Bensaid, T.A. Meynard, Multicell converters: active control and observation of flying-caacitor voltages, IEEE Transactions on Industrial Electronics, Volume 49, Issue 5, ag , 200 [5] K. Benmansour, J. Deleon, M. Djemai, Adative observer for multi-cell choer, Second International Symosium on Communications, Control and Signal Processing ISCCSP, Marakesh, Morocco, 2006 [6] W.Perruquetti, J.P. Barbot, Sliding mode control in engineering, CRC Press, 2002 [7] T. Meynard, M. Fadel, N. Aouda, Modeling of multilevel converters, IEEE Trans. Ind. Electron., vol. 44, , June 997.