A Methodology for High-Power Drives Emulation Using a Back-to-Back Configuration

Validation of high-power converters at the development stage often cannot be performed using the real load. A testbench consisting of the Equipment Under Test (i.e., tested power converter) and an auxiliary power converter, preferably using power recirculation, can be used instead. A challenge for correct testing using this approach comes from the fact that the harmonic content of the currents can significantly differ between the testbench and the real system. This might strongly affect the loading of power switching devices compromising the reliability of the validation process. This paper proposes a methodology to select the operating conditions of both tested and auxiliary converters in the testbench to resemble a given operating condition of the actual system. Since identical behavior is not generally possible, a cost function will be used to trade-off among different factors (i.e., fundamental current magnitude and phase, harmonic content, etc.). The proposed approach evaluates a large number (hundreds of thousands) of testbench operating points in a few seconds and selects those which minimize the cost function. In a later stage, the selected points can be validated using detailed dynamic simulation. The selected conditions can then be used to test the converter in the testbench emulating the real system behavior in a given operating point condition. The proposed methodology was developed for railway electric drives but can be extended to other applications.

INDEX TERMS Railway traction drive, machine emulation, back-to-back inverters, current harmonics, power recirculation, high-power converter testbench. EUT power factor. 19 Same cases apply for currents by replacing v/V and i/I . 20 Same cases apply for AUX inverter by replacing EUT by 21 AUX. 22 Variables denoted by prime refers to testbench parameters. 23 24 Validation of high-power converters at the development 25 stage is a challenging task [1]. On one hand, often it can- 26 not be performed using the real load. On the other, power 27 fundamental current, power factor) match those expected for 48 the real system is relatively easy to achieve. However, this 49 approach neglects the fact that the harmonic content of the 50 currents for the real system and testbench can significantly   [16], [17], [18], [19], ther complexity [20], [21], [22], [23]. Most machine emu-72 lators reported in the literature use PWM modulation with 73 switching frequency in the order of tens of kHz [7], [16], 74 [19], [24] where the switching harmonics introduced by the 75 AUX inverter are easily filtered since these harmonics have 76 higher frequencies compared to the fundamental component. 77 In those cases, the same fundamental current magnitude can 78 be guaranteed, the harmonic content of the current being less 79 relevant. This is not the case for synchronous modulation 80 techniques used in high-power drives that operate with very 81 low switching-to-fundamental frequency ratios [20], [25] 82 where switching harmonics occur at relatively low frequen-83 cies (5th, 7th, 11th, etc.). In these cases, it is not possible to 84 achieve equal current harmonics and at the same time equal 85 current magnitude as will be demonstrated in this paper. 86 Another challenging aspect that is not properly addressed 87 in the literature, is the selection of the filter inductance 88 coupling the EUT and AUX inverters (see Fig. 1). In [3], 89 it is indicated that filter inductance should be equal to the 90 machine stator leakage inductance to make the emulation 91 inverter output voltage a direct representation of the machine 92 back emf. However, this approach neglects the effects due 93 to harmonics injected by the AUX inverter. In [26], it is rec-94 ommended that the filter inductance value should be higher 95 than the machine stator transient inductance value in order 96 to compensate for the imposed emulation inverter harmonics 97 and get a comparable THD to the real motor case. A value of 98 70 µH was selected for a testbench of power in the range of 99 40 kW, however, it is not indicated on which basis this value 100 was chosen. In the proposed methodology, it is possible to 101 identify the value of the inductance which provides the best 102 matching of harmonic content and/or peak current.

103
To the best of the author's knowledge, previous works do 104 not consider the influence of both the harmonics injected 105 by the AUX inverter and filter selection on the harmonic 106 content or peak current of EUT currents. This can result in 107 significant differences with respect to the real application 108 in the operating conditions and stresses of power-switching 109 devices [27], [28]. Instead of trying to precisely reproduce 110 in the testbench the operating conditions of the real system 111 at the fundamental frequency (i.e., same fundamental voltage 112 and current), some degree of freedom could be allowed in 113 the selection of the operating mode of EUT and AUX con-114 verters. This degree of freedom would be used to increase the 115 similarity between the current handled by the EUT devices in 116 the testbench and the real system by considering both current 117 harmonics and peak current. Detailed dynamic simulations 118 could be used for this purpose. However, the number of cases 119 that can be evaluated by simulation will be limited, as they are 120 computationally time-consuming. This will compromise the 121 level of optimization that can be achieved using this approach. 122 This paper proposes a methodology to find the operating 123 point of a testbench which minimizes the differences with 124 respect to a selected operating point of interest in the actual 125 drive. Advantages of the proposed methodology compared to 126 literature are: 1) allowing changes of drive modulation strat-127 egy, power topology and testbench filter inductance value. 128 2) Identifying the best filter inductance value to achieve 129 VOLUME 10, 2022 the best matching between the real drive and the testbench.
tions. 3) Implementation in the testbench of the optimal solu-144 tion(s). The proposed methodology is especially well suited 145 for high-power drives using synchronous modulation meth-146 ods, though it can be applied to asynchronous PWM/SVM 147 as well. The method can also be applied to any type of AC 148 machine where the main objective is testing the devices in 149 steady-state operation.

150
It is remarked on the importance of testing passive compo-151 nents (i.e., dc-link capacitors, busbar, etc.) under real system 152 operation conditions. For high-power industrial drives, this 153 process is done separately from the power electronic con-154 verter since power recirculation is usually used to decrease 155 consumption and avoid energy waste. In this context, the 156 same methodology proposed in this paper can be applied to 157 test passive components. However, this remains out of the 158 scope of this paper as the main focus is emulating stresses 159 on power-switching devices.

160
The paper is organized as follows. Real system is 161 described in Section II; testbench description and require-162 ments are addressed in Section III; cost function is defined in 163 Section IV; analytical models used for system emulation are   Fig. 2b shows a two-level (2L) inverter which will also 173 be discussed in this work. Fig. 3 shows a typical voltage vs. techniques are used at medium and high speeds [21], [29], 179 [30]. The reason for this is that railway traction inverter manu-  modulation strategies along the speed profile. The paper is 185 focused on the high-power operation of traction inverters at 186 high speed where synchronous modulation is used because in 187 this case harmonics injected by the emulation inverter can no 188 longer be neglected which adds further complexity.

189
The voltage applied by the EUT to the IM can be repre-190 sented using complex vector notation as (1): All the following discussion will assume that the sys-193 tem is in steady state. For this case, (1) can be split into 194 fundamental voltage v f and harmonics v h (2), with h = 195 −5, 7, −11, 13, . . . for the usual modulation methods.
The fundamental voltage v EUT f is defined by both the 198 modulation index M EUT (see Fig. 4) and the fundamental 199     Fig. 5a).

233
The IM will be replaced by an auxiliary (AUX) inverter in 234 the testbench, as shown in Fig. 1. EUT and AUX inverters 235 are connected back-to-back (B2B) through an inductor, power 236 being recirculated through the dc link. The target of the 237 testbench is to accurately reproduce the operating conditions 238 of the EUT in the real system in Fig. 2.

239
Defining the real axis to be aligned with EUT inverter 240 fundamental voltage V EUT f (see Fig. 6b), then for the B2B 241 testbench: Superposition will be also used to analyze the behavior of 246 harmonic currents in the testbench. Fig. 5b shows the decom-247 position of B2B into fundamental and harmonic subcircuits. 248 Two subcircuits are needed in this case to account for the 249 harmonics produced by EUT and AUX inverters.

250
The following conditions can be established regarding the 251 testbench operation: 252 1) To achieve the desired fundamental current, AUX 253 should produce a fundamental voltage given by (10), 254 with ω f being the fundamental frequency and L the 255 testbench filter inductance. It is noted that since the 256 proposed method is intended for high values of the ω f 257 (SHE region in Fig. 3), filter resistance R can be safely 258 neglected. 259 2) To match the harmonic content of the currents of 261 testbench (I B2B h ) and real system (I EUT h ), the AUX 262 inverter should inject the voltage harmonics required to 263 compensate for the different values of the inductance 264 of machine L σ s and testbench L (resistances being 265 neglected in this case); (11) holds in this case.
3) The AUX inverter should not produce frequency com-268 ponents at frequencies different from those produced 269 by EUT (or should be negligible). Unwanted current 270 harmonics would circulate through EUT inverter other-271 wise, modifying its electrical and thermal behavior.

272
All these conditions could be achieved by operating the 273 AUX inverter using PWM with a high switching frequency. 274 In this case, the voltage commanded to the AUX inverter 275 would include the fundamental and harmonic voltages needed 276 to achieve the desired currents. Voltage harmonics due to the 277 AUX inverter would be filtered off by the testbench induc-278 tance L, provided that its switching frequency is high enough. 279 While this approach might be feasible for low power systems, 280 it is not viable in general for high power converters, as thermal 281 limits make unfeasible the use of high switching frequencies 282 for AUX inverters. 283 VOLUME 10, 2022 FIGURE 5. Decomposition of system circuits using superposition (a) EUT inverter and IM, (b) B2B connection of EUT and AUX inverters. L m , L ls and L lr are the magnetizing and leakage inductances, R s and R r are the resistances, s is the slip, R s1 and L σ s are the stator transient resistance and inductance, L is testbench filter inductance, R is parasitic resistance of L. Variables denoted by prime in (b) refer to testbench parameters. It is concluded from the preceding discussion that the volt-284 age produced by the AUX inverter in Fig. 1 can be modeled 285 as (12) and (13) (see Fig. 6b-6d). 287

288
Same as for the EUT, voltage harmonics will be a function 289 of the modulation index and modulation strategy. The result-290 ing current will be of the form shown in (14); the condition 291 to exactly reproduce in the testbench the operating conditions 292 of the real system would be (15).
Under the premise that AUX inverters cannot switch sig-296 nificantly faster than EUT inverters, condition 1) is easily 297 achieved by proper selection of M AUX and α AUX in (13). 298 Condition 3) is achieved by using a modulation strategy in 299 the AUX inverter which produces harmonics at the same 300 frequencies as EUT. However, the voltage harmonics injected 301 by the AUX inverter will not comply in general with (11), 302 meaning that condition 2), and consequently (15), will not 303 be satisfied.

305
It is concluded from the previous discussion that it is not pos-306 sible to achieve in the testbench both the same fundamental 307 and harmonic currents of the real system. A cost function C 308 (16) can be used to objectively assess the level of similarity 309 between the testbench and the real system.
γ h , γ ϕ and γ M being the weighting factors of current 313 harmonic components, power factor and modulation index 314 respectively. Selection of these weighting factors is done 315 according to the priorities and concerns of each application 316 (values for analyzed cases being shown in Table 3).

317
The objective is to select the operating point of EUT and 318 AUX inverters which minimizes C. Constraints and targets 319 used to define C are the following: 320 • Fundamental current magnitude and fundamental fre-321 quency will be forced to be the same for the real 322 system and the testbench (17). Consequently, they are 323 not included in the cost function. 324 Solutions for (17) can be easily found from the vec-326 tor diagram in Fig. 6. Known the desired fundamental 327 current and the inductance L connecting EUT and AUX 328 inverters, the required differential voltage magnitude is 329 obtained by (18). will not require time consuming dynamic simulations but fast 375 analytical calculations. Due to this, hundreds of thousands of 376 operating conditions can be evaluated in seconds.

V. SYSTEM EMULATION USING ANALYTICAL FUNCTIONS 378
If the harmonic content of the voltage being applied by EUT 379 and AUX inverters is known, the resulting current harmonics 380 can be obtained for different values of h by using (20).
Two cases can be distinguished: 383 1) For asynchronous PWM/SVM methods, the harmonic 384 content will depend on the modulation index, fun-385 damental frequency and switching frequency. Inter-386 modulation harmonics will occur in this case. These 387 harmonics can be especially harmful and difficult to 388 model when switching and fundamental frequencies 389 are relatively close to each other.

390
2) For synchronous modulation methods, the harmonic 391 content is only a function of the modulation index, 392 which significantly eases the analysis. Interest-393 ingly, operation with synchronous modulation and 394 low-switching frequency is the most difficult to repro-395 duce in the testbench.

396
Synchronous modulation methods will be the target of 397 the analysis presented following. Two different modulation 398 strategies will be considered to exemplify the process: SHE 399 with one angle (SHE1) and two angles (SHE2) [32], [33]. The 400 phase voltage waveforms for these modulation techniques are 401 shown in Fig. 7.  Fig. 2a using SHE1. For all the figures 406 shown in this section, voltage is given in per unit (p.u.) of 2v dc π . 407 Each spectrum was obtained from a dynamic simulation using 408 VOLUME 10, 2022  The same process can be followed for the case of a 3L 421 inverter using SHE2. The frequency spectrum of the voltage 422 will include the same harmonics as in Fig. 8. However, they 423 will be a function of modulation index and first commutation 424 angle α 1 . In is noted that the second commutation angle of 425 SHE2 α 2 is not an independent variable, but depends on 426 modulation index and α 1 as shown by (22) [33]. Therefore, 427 each voltage harmonic injected by the inverter must be stored 428 now in a two-dimensional LUT, as shown in Fig. 9.
The same process can be followed for a 2L inverter in 431 Fig. 2b. Fig. 10 shows the magnitude of the harmonics vs. 432 modulation index when using SHE1 (see Fig. 7-c).   process is as follows (encircled number refers to the stages 442 shown in Fig. 12): 443 1 Once the desired operating point of EUT+IM is 444 selected, this will determine EUT modulation index M EUT 445 and fundamental frequency ω f , as well as motor speed. 446  It is noted that the limits for V f vary according to V EUT f 457 and the used filter inductance value (see (18), (19)). The AUX 458 inverter voltage is obtained as (24), its phase angle being (25).
It is noted that the harmonic h of the AUX inverter read 475 from LUTs must be rotated as shown by (27).
For each V EUT f , V f set, the cost function C 478 is obtained using (16). The weighting factors are calcu-479 lated using (28), (29). According to the selected criteria for 480 this analysis, the current harmonic components are assigned 481 weights inversely proportional to the harmonic order, giving 482 the fifth component the highest weight where the total weight 483 is one. The minimum computed value of the cost function 484 defines the operating point of the B2B which provides the best 485 agreement with the real system EUT+IM.  Table 1. Using these parameters, detailed simulation models 500 are developed using MATLAB/Simulink to precisely model 501 the real motor and drive. It is remarked that the B2B con-502 figuration is totally reversible providing functionality in the 503 four machine quadrants. Results are shown for forward motor 504 quadrant only since reverse motoring would not show any 505 difference in current harmonic content. In this case, current 506 and voltage vectors would have the same magnitude and 507 phase but with opposite direction. Selected operating point 508 for the EUT+IM system is given in Table 2 in forward motor 509 and generator modes of operation. The resulting current wave 510     Table 1. Modulation strategies for EUT and AUX inverters and cost function weights for (A) -(D) cases are shown in Table 3. shape obtained by means of dynamic simulation is shown in   The coefficients selected for the calculation of the cost 527 function are shown in Table 3-Case A. Note that only the 528 magnitude of current harmonics was considered. The cost 529 function results for the value of the inductance L in Fig. 14 530 are shown in Fig. 15c).

531
A sweep of the filter inductance value was performed in 532 order to assess its impact on the cost function. This approach 533 can be used to select the most adequate value of inductance 534 for a given operating point. Fig. 15 shows the cost function C 535 results for the available values of inductor L. Fig. 16 shows 536 the optimum of the cost function for each value of L in the 537 (M EUT , V f ) plane. Fig. 17-Case (A) (red trace) shows 538 the optimal cost function value in terms of L, the minimum 539 occurring for L = 1.782 mH.

540
To verify the results of the optimization process, the phase 541 current for the optimal B2B operating point was obtained 542 by means of dynamic simulation. Currents for the EUT+IM 543 and B2B are shown in Fig. 13-Case (A). The cost function 544 obtained using dynamic simulation results showed an excel-545 lent agreement with the value from the analytical approach. 546 It is interesting to note that regardless of the small value of the 547 cost function, differences between the currents for EUT+IM 548 and B2B cases in Fig. 13-Case (A) are relevant. The reason for 549 this is that only current harmonics magnitude was considered 550 to obtain C, phase angles were disregarded. A result of this is 551 that the peak current for B2B case is significantly smaller than 552 peak current for EUT+IM case, as shown in Fig. 18 (traces 553 in red).

554
Optimization process was repeated considering both 555 magnitude and phase of current harmonics using the weight 556 coefficients in Table 3-Case (B). Modulation index and power 557 factor are disregarded in this case. Traces in blue in Fig. 17 558 and Fig. 18 show C min and peak current for the different 559 values of L. The lowest value of C min occurs for L = 560 3.564 mH, but it is significantly larger compared to Case (A). 561 Fig. 13-Case (B) shows the current for the B2B obtained 562 by means of a dynamic simulation. Differences between 563 EUT+IM and B2B cases are still relevant.

564
To improve the similarity between EUT+IM and B2B 565 cases, SHE2 was used with AUX inverter [Case (C) in 566 Table 3]. It is noted that this implies higher switching losses 567 in AUX inverter. Fig. 17 and Fig. 18 (magenta trace) shows 568 C min and peak current vs. L, the minimum of C min occurring 569 for L = 3.564 mH. Fig. 13-Case (C) shows the current for 570 EUT+IM and B2B configurations at C min , a slight improve-571 ment being observed with respect to Cases (A) and (B). 572 Finally, results when SHE2 is used in EUT+IM system 573 are shown in Fig. 13, Fig. 17 and Fig. 18 (black trace) 574 respectively. Weight coefficients are shown in Table 3-Case 575 (D). C min as well as the smallest error in the peak current are 576 now obtained for L = 7.13 mH [point(5)]. Consistently with 577 these results, a better agreement between current waveform 578 of EUT+IM and B2B is observed in this case in Fig.13.

579
It is interesting to see that the points with the best peak 580 current matching (i.e., points(1) and (2) Fig.18) have the 581 worst harmonic content matching (Fig.17) while the optimal 582

603
A B2B scaled-down testbench following the schematic dia-604 gram of Fig. 19 was developed as shown in Fig. 20. The 605 characteristics of the testbench are shown in Table 4. It is 606 VOLUME 10, 2022   Table 3.  Table 3. noted that a full-rated testbench for the final application is 607 being constructed by Ingeteam Power Technology.

608
The real drive is developed following the schematic dia-  Table 4. The operating point given 611 in Table 5       can be carried out as described in Fig. 12. Both magnitude and 623 phase of current harmonics are considered using the weight 624 coefficients shown in Table 3 Table 5). The 627 predicted optimal B2B operating point (i.e., C min ) is shown in 628 Table 6. of EUT and AUX is small (see Table 6 and Fig. 22). This is due   as a premise. Better matching of current harmonics could 654 be achieved if the condition in (17) is removed, i.e., error 655 of the fundamental current is included in the cost function. 656 Changes to the cost function can be applied to better suit 657 specific requirements of the application of interest. It is noted 658 that the frequency resolution obtained in the FFT analysis 659 is 50 Hz and the Nyquist frequency is 500 kHz (sampling 660 rate of 1 MS/s), which are enough to capture the fundamental 661 frequency used in the paper (100 Hz), and the harmonic 662 components considered (-5, 7, -11, and 13), and avoiding the 663 risk of aliasing.

664
Finally, it is worth remarking that, for the testbench in a 665 B2B configuration, a startup procedure is necessary to avoid 666 undesired transients which may jeopardize the devices. In this 667 case, a startup process is implemented based on ramping the 668 commanded modulation indices as well as the angle between 669 VOLUME 10, 2022 the fundamental voltage components of both EUT and AUX inverters, α AUX .