Modified vector control appropriate for synthesis of all-purpose controller for grid-connected converters

Modified vector control appropriate for synthesis of all-purpose controller for grid-connected converters Tihoir Čihak dipl.ing., Mladen Puškarić M.Sc.E.E. KONČAR Electrical Engineering Institute Inc. Fallerovo šetalište, 1000 Zagreb, Croatia Ph.D., E.E. Željko Jakopović Faculty of Electrical Engineering and Coputing Unska 3, 10000 Zagreb, Croatia Abstract Vector control and its application in power electronic converters, specifically grid connected inverters and rectifiers is well known topic. Nuerous books and articles covered any of its probles and features, but ostly in theoretical way, without taking into account liited coputing resources of converter control syste, real-life syste paraeters which can differ fro the siplified odels used in theoretical analysis and appearance of new paraeters as a consequence of concatenating converter with other converters, filters, transforers and other eleents. Ipleentation of vector control in real-life converter is therefore not as straightforward as it ay see. Advanced filter and copensation eleents can be hard to ipleent in a DSP syste on one hand and siplified control structures can lead to unstable syste or one that does not fulfil necessary requireents on the other hand. This article shows several odifications to siple voltage oriented vector control in threephase grid connected inverter which handles probles which occur due to connection of transforer between the grid and the converter, but also shows that odifications which have been carried out lead to universally applicable vector control syste for grid connected converters. Keywords power converters, vector control, renewable energy syste, power quality, converter siulation odel I. INTRODUCTION Modern power electronic converters are, non-dependent on the seiconductor switch technology that they use, essentially unfeasible without a fast and precise control syste. Many requireents need to be fulfilled, for instance power factor correction requireents and low values of inrush currents in controlled rectifiers, strictly controlled current haronic coposition and fault ride-through capability in grid connected inverters. Such requireents need odern DSP processors, alone or coupled with FPGA devices, to be achievable. Since these devices are in use, nuerous proble solving control algoriths have been invented, fro DTC (Direct Torque control) to neural network based control algoriths [16]. Although any of the see to be an ideal solution to particular proble, practical ipleentation can be probleatic or ipossible due to liited processing resources. With good coproise between coplexity, good perforance and ease of tuning one control ethod iposed itself as default control syste for grid connected PWM converters. Vector control, or ore specifically voltage oriented vector control, shown generally in Fig., is chosen based on several positive features it posses [4]. Although it is basically a siple and well known control ethod, in practical ipleentations any probles regularly appear, ost of the not explained in literature in detail. This article will show how to easily circuvent probles that arise fro connection of three phase transforer between the basic, typically chosen, PWM inverter and grid. Shown solutions are ipleented as add-ons in the control structure in that way that the resulting controller can be used as a ore general controller, adaptable to different output topologies found in practice. Also, soe iportant notes on the transducer placeent are given. II. PROPOSED CONTROL SYSTEM Basic idea behind the control syste shown further on is to create a syste which can be, with the correct transducer placeent, used universally, regardless of the nuber and character of the filter coponents between the converter power block and the grid. Adaptation to the specific filtering chain shall be done through disabling the unnecessary controller parts by software paraeters rather than changing the controller structure altogether. The core of the controller ust be fixed and well defined to allow such changes. Industry trends in converter design favor siplicity and iniization of coponent nuber which eventually lead to lower end prices but on the other hand coplicate control algoriths. Typical exaples are grid connected inverters for renewable energy sources, as for instance central PV inverters. A typical converter design for such application is shown on diagra in Fig. 1. The DC input passes through the protection and switching equipent (1), into the DC link capacitors () and switching block (3). For ediu to high power converters, seiconductor block is usually of a three IGBT half-bridge design with one or ore IGBTs in parallel depending on the required power [14]. Three phase output is then directed to the output filter (4) which can be of L, LC or ultistage filter bank type (ephasized with dashed line after the point (D)). Filtering chain can end either with previously entioned coponent or another inductor of transforer (5). Converter is connected to the grid through another set of protection and switching equipent. This article uses LC filter terinated with a transforer as an exaple. Transducers can be positioned in a nuber of ways in converter chain [4]. DC easureents are, as shown in Fig. 1, positioned at point (A), with additional DC easureents at (B) if the topology, e.g. three level converters, requires it. On 43

Fig. 1. Converter block diagra. Fig. 3. Used transforer equivalent odel. III. SYNTHESIS OF COMPENSATION BLOCKS As it can be seen in Fig. 4, power transforers rotate phasors according to their vector group. This is true for both current and voltages. As for the easured voltages, if the transducer position is on point (F) in Fig. 1 this is easily accoplished with fixed angle offset in DQ transforations. According to Fig. 3, a set of equations that describes a transforer and its behavior can be written as: Fig.. Block diagra of voltage oriented vector control. the output side, since correct control of electric variables is required on the interface between the converter and the grid, it would be logical to place transducers at the point (F), but fro the controller tuning standpoint [17][18][19], transducers should be placed as close as possible to the (C). In general, positioning current transducers at (C), and voltage transducers at (F) allows for fast current control and the correct estiation of the voltage state in the grid, which akes the control syste universal. The downside of this approach is that paraeters of all the passive coponents after the current sensors ust be known and copensated for, and any voltage phasor rotation and reduction ust be taken into account. Terination of the converter chain with a transforer differs by a great aount fro the typical connection of the converter to the grid directly, through one of filter topologies described in the literature [4][9][15]. This is clearly seen if a converter with a LC filter is connected to the transforer. To explain the influence of the transforer, a variation of a T- odel equivalent circuit shown in the Fig. 3 will be used. With transforer at the end of the converter chain, filter topology becoes uch ore coplex, requiring copensation of extra eleents. Furtherore, a cross coponent, transforer agnetization current I 0 occurs and needs to be copensated. Siilar current offset coponents exist on every LC filter node. Paraeters required for copensation can be found through siple transforer testing [13]. Also, typical three phase output transforers have phase angle rotation between priary and secondary winding, usually in for of Dy vector group, iproving current haronic content in that way [13] [0]. Such phase rotation needs to be taken into account with proposed current transducer position. In effect, the D and Q current coponents on the secondary side ust be expressed as a su of the D and Q current coponents on the priary side if controller topology ust not be changed. This is shown in Fig. 4 for D current coponent only. The sae is true for the Q current coponent. i =i i = i P - (1) G I 0 1 1 i = i u + u R ωl G P G G ; I P control OFF G G () 1 1 = u + u (3) R ωl As the basic requireent on the copensations structure is that the copensation ust be added in such way that the basic control structure is not changed, (1) and () are rewritten. The controllers are synthesized in DQ syste which leads to siple structures essentially controlling DC values. Therefore, an assuption is ade that for each operating point the syste will reach stationary point at which the output is fixed and directly proportional to the reference value: cop ( i 0) i δ = i + I I + I control control OFF REF OFF In other words, the exact controller output is not observed, but a known agnetization current is added to the set (reference) current as an offset current. Equations () and (4) can now be expressed in DQ syste as follows: (4) 1 1 i = OFF DQ ug DQ j ug DQ R ωl (5) 1 1 i = OFF D ugd ugq R + ωl (6) 1 1 i = OFF Q ugq ugd R ωl (7) Equations (6) and (7) now show a set of expressions applicable to standard vector control. One distinctive feature of 44

Fig. 5. Block diagra of proposed control syste odifications. For a filtering syste that can be approxiated as a LCL filter, output current can be expressed as: Fig. 4. DQ current coponent coupling on Dy transforer (D coponent).. these expressions is the use of the transfored grid side voltages which are known if proposed transducer positions are used. By describing the transforer in this way, copensation can be added as an additional reference coponent as shown in Fig. 5. Care ust be taken when using previous equations; firstly, they iply that the other coponents prior to the transforer are already copensated. Secondly, an assuption that the transforer can be represented with a set of linear coponents is ade. This will be generally true, but if this is not the case in particular ipleentation, different ethods ust be used [1]. The ter cross-coupling coponents assues control coponents which negate influence of inductive eleents in perpendicular axis [4][1]. In practice, in ost of the cases they ignore the influence of filter cross coponents and the total resistance of coponents connected to the inverter output. For the cases where capacitor influence can be neglected for a whole ultistage filter, these coponents are defined as: ( 1... ) D ( R1 +... Rn Rt eqv) u = u i L + + L + L ω ff D D Q n t eqv + i + + ( 1... ) Q ( R1 +... Rn Rt eqv) u = u + i L + + L + L ω ff Q Q D n t eqv + i + + These coponents are added as feedforward as shown in Fig. 5. If the current flow through transversal filter coponents can t be neglected, (8) and (9) are not true as the current will change with each consecutive filter stage. Incorporating these influences will require either additional transducers or additional DSP coputational capacity. Therefore, for practical ipleentations, with regard to previous, care ust be taken when selecting filtering coponents. For cases where copensation is still required, but without additional current or voltage transducers, a siple concept can be used. (8) (9) ( 1 ω 1 ) ( ω ) i i L C u j C = (10) PC DQ P DQ DQ ( 1 ω 1 ) i = i L C + u ωc (11) PC D P D set Q ( 1 ω 1 ) i = i L C u ωc (1) PCQ PQ set D For special cases, derating expressed in brackets in (10) to (1) can be approxiated as: ( ω L1C) 1 1 (13) i i + u ωc (14) PC D P D set Q i i u ωc (15) PCQ PQ set D According to (14) and (15), the current at the second filter stage can be expressed using filter paraeters, easured current at the output of the inverter and voltages at the inverter output. These voltages are known fro the controller set voltages for the PWM odulation [4][17][19]. By using such copensation, (8) and (9) will necessarily change. Using the known facts on PID controllers [1][][3], for each operating point, when the syste reaches stationary state, current through the first filter coponent will be equal to the easured current, while at the output of the filter coponent (input of the next filter stage) current will be equal to the noncopensated reference current expressed in (14) and (15). IV. IMPLEMENTATION Developed theoretical groundwork was ipleented and tested on a coercial central PV inverter shown in Fig. 6. Inverter is of single stage, grid connected topology with galvanic isolation using output transforer. Inverter is of odular design; it can operate as stand-alone unit or in parallel with identical units on a single transforer for higher output. Testing was done on a stand-alone type. Due to its single-stage topology and control concept with cascaded controllers it proved to be an ideal object for testing of vector control odifications on the grid side part of the control algoriths. 45

TABLE I. KONSOL-150 TECHNICAL DATA Absolute axiu input voltage 1000V MPPT voltage range 410V 800V Operational voltage range 380V 830V Maxiu input current 400A Noinal power 150kW @ cos φ=1 Noinal voltage 3 380/400V RMS Noinal current 3 17A RMS Fig. 6. KonSol-150 central PV inverter. Control concept allowed disabling algorith parts that were of no interest for this research without influence on the inverter operation. Soe of the technical specifications of the inverter are given in table 1. Control hardware is a custo ebedded control syste designed as a two-board syste. One is a CPU part of the syste, and the other is a easureent acquisition and filtering board. The CPU board contains the ain DSP coupled with FPGA coponent and slave DSP. For this research, all algorith coponents were ipleented in the ain DSP. For testing purposes, to avoid isinterpretation of the results, only the grid interface with vector oriented algorith and grid synchronization with PLL was enabled. To assure correct assessent of the syste operation, DC and AC connections with fixed operating points have been provided with a setup shown in Fig. 7. Setup consists of a set of DC generators (only one was used) with output voltage in the range fro 0-550V DC and noinal current of 454A DC. In series with generator is a set of adjustable high-power resistors which can be bypassed. Resistors serve as a protection device which liits the axiu input current and to soften the otherwise hard output characteristic of the DC generator. On the AC side, two different sources were used, rotating transforer (3 0-760V AC ) for safety reasons, to allow for testing of algorith at low voltages, and a distribution grid for currents up to 1000A at the connection point. Measureents were done with data acquisition syste with external easureent transducers. V. RESULTS Several tests were done on the PV inverter to validate the copensation algoriths and investigate the syste behavior. Since any protection sequences were disabled to allow for experientation with the algorith and inverter paraeters, due to safety reasons, operating points under the noinal power were chosen. Input voltage was liited to 500V (open circuit voltage). On the AC side, coissioning was done at half of the noinal voltage and after confiration of correct operation, testing was done with noinal output voltage. Fig. 8 shows output current and phase voltage for syste with copensations. This can be considered reference state for the inverter as it is easured at two thirds of the noinal power Fig. 7. Inverter easureent setup. and doesn t change qualitatively up to the noinal inverter power. For a clearer view, picture also shows phasor view of easured values. It is shown directly, as calculated in the data acquisition syste, without any post processing. Slight offset (asyetry) seen on soe phasor diagras is calculation error due to easureent transducer non-ideality, data acquisition processing speed and influence of other loads on the power line. Resulting power factor is shown nuerically. A set of tests was done to observe syste behavior when transforer paraeters are iscalculated. First, syste behavior with iscalculation of the transforer odel equivalent resistance was observed. Miscalculation was siulated by changing the R coponent value in DSP application into R /4 and 4 R respectively. Fig. 9 shows power factor changes for this test. As the equivalent resistance enters the copensation calculation as a denoinator, power factor does not change linearly. Siilar testing was done for the transforer odel equivalent agnetizing inductance. Fig. 10 shows resulting changes in power factor. Nonlinear change is observed due to sae reasons as in the previous test. Miscalculation was siulated by changing the noinal value of factor ω L which is changed into (ω L)/ and (ω L) respectively. During both tests no stability probles were found. Next, a throughout evaluation of copensation coponents, including copensation of transversal filter coponents was carried out. Testing was done for every cobination of algorith odifications in operating points that were fixed and coparable between tests. Operating points were chosen according to RMS output current. As representative, 5A RMS operating point is shown. Fig. 11 shows output current and phase voltage for syste with all copensations (power factor given nuerically). Soe differences to reference output in Fig. 8 can be observed due to the fact that at chosen operating point inverter is at only 10% of noinal power output. This operating point can be considered worst case for the inverter. This clai supports the fact that ost coercial products (central PV inverters) don t have declared values of efficiency, THD and power factor under half of the noinal power. Fig. 1 shows the syste state with the transforer copensation disabled, while on the Fig. 13 output filter copensation is disabled. As expected, influence of the transforer copensation is uch 46

Fig. 8. Inverter output at 150 A RMS with full copensation. Fig. 9. Power factor change during siulation of R iscalculation. Fig. 10. Power factor change during siulation of ω L iscalculation. Fig. 11. Syste with all copensations enabled, 5A RMS current. Fig. 1. Syste with disabled transforer copensation, 5A RMS current. Fig. 13. Syste with disabled filter offset copensation, 5A RMS current. Fig. 14. Syste with all copensations disabled, 5 A RMS current. higher than filtering capacitor copensation. But, as results in Fig. 14 show, when all copensation loops are disabled the resulting power factor changes uch ore than in previous tests. This is due to fact that errors ade at the beginning of the controller chain are passed into subsequent control loops and the errors are being agnified and second, under low load syste paraeters are increasingly non-ideal with ore pronounced nonlinearities in the output. Nuerically, copensation loops will change the inner reference currents. For a broader and clearer view on influence of the copensation loops, tests have been ade in a wide range, fro inverter idle to 80% of the noinal power, with 5A RMS output current steps. Influence of copensation eleents are plotted relative to the non-copensated reference current in 47

REFERENCES Fig. 15. Copensation aount in percentage referring to non-copensated reference currents in D and Q axis. Fig. 16. Power factor change in percentage referring to full-copensation. Fig. 15. 100% of current is equal to reference currents without copensation. Copensation sign is relative to noncopensated reference. Due to easureent error and transducer noise, easureents under 5A RMS are oitted. VI. CONCLUSION The assuptions presented at the beginning of this work, that filter and power transforer paraeters can be successfully incorporated in the voltage oriented vector control without changing its basic structure are shown through theoretical groundwork which is tested an verified on a real central PV inverter. Presented results show that vector oriented control odifications are successfully ipleented and give observable iproveent. Also, easured data shows copensation influence throughout the inverter power range. This on one hand shows interdependence of copensation eleents and on the other hand it shows in which parts of the inverter power range copensation ust be used and parts where approxiations used in existing literature are true and can be used safely. Such inforation, as seen fro results, is especially iportant for power converters that operate at lowload for ost of the tie, i.e. PV inverters, as current nors suggest [4]. For future work, shown control odifications will be further expanded into copensation syste for an arbitrary nuber of filtering coponents prior to the output filter or transforer. This expansion will feature reduction of arbitrary nuber of filtering coponents into shown structure and autoatic paraeter deterination. This odification will also be ipleented and tested on a real inverter. [1] H.-T. Neisius, I. Dzafic, Three-Phase Transforer Modeling using Syetrical Coponents, 17th Power Systes Coputation Conference, Stockhol Sweden, August 011 [] J. Dannehl, F.W. 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