The Use of Voltage Transformers for the Measurement of Power System Subharmonics in Compliance With International Standards

The measurement of subharmonics in distribution systems requires instrument transformers to reduce voltage and current to levels fitting with the low-voltage input of the power quality (PQ) instruments. The in-force international standards establish algorithms and methods for detecting, measuring, and reporting subharmonics. In particular, the IEC 61000-4-7 suggests performing the discrete Fourier transform over basic time frames of ten cycles (12 cycles) for the 50-Hz (60 Hz) power frequency. Considering the case of 50-Hz constant power frequency, the spectral analysis is performed with a fixed spectral resolution of 5 Hz; thus, subharmonics with a frequency not integer multiple of 5 Hz could introduce inaccuracies in the measurements because of the spectral leakage. In this framework, this article investigates the additional error contributions that can be introduced by voltage transformers (VTs) used, at the input of PQ instruments, to measure subharmonics in compliance with international standards. The analysis is conducted through numerical simulations and experimental tests on two commercial VTs based on different operating principles. Results show that the use of a VT to measure subharmonics, in compliance with international standards, could introduce higher additional errors compared to the ratio errors of the same device evaluated at subharmonic frequencies.


28
T HE large-scale introduction of distributed generation sys- 29 tems based on renewable sources and the spreading of 30 electronic loads is turning the power grids into increasingly 31 complex systems characterized by increasing disturbances. Giovanni D'Avanzo is with the Dipartimento Tecnologie di trasmissione e distribuzione (TTD), Ricerca sul Sistema Energetico S.p.A., 20134 Milan, Italy, and also with the Dipartimento di Ingegneria, Università degli Studi della Campania "Luigi Vanvitelli," 81031 Aversa, Italy (e-mail: giovanni.davanzo@rse-web.it).
Digital Object Identifier 10.110910. /TIM.2022 In this scenario, the accurate monitoring of power quality (PQ) 33 parameters is gaining more and more importance [1], [2], [3], 34 and several international standards [ The measurement chain for PQ monitoring in medium-37 voltage (MV) and high-voltage (HV) systems commonly 38 includes instrument transformers (ITs) to scale the voltage 39 and current to levels fitting with the input of PQ instruments 40 (PQIs). Nevertheless, the performance of ITs in the presence 41 of PQ phenomena represents an issue only partially addressed 42 in the literature [10], [11], [12], [13] and technical reports 43 [14]. 44 Among the PQ phenomena, the monitoring of harmonics 45 and interharmonics plays a crucial role because their presence 46 causes many problems, such as overheating of conductors, 47 losses in power transformers, improper functioning of electric 48 motors, and damage to power factor capacitors. 49 Subharmonics are particular cases of interharmonics; 50 in fact, they are defined as components with frequen-51 cies lower and, consequently, not integer multiples of 52 the fundamental frequency at which the supply system is 53 designed to operate. Subharmonics are injected into the 54 power grid by distributed generation systems, such as wind 55 farms [15], [16], hydropowers [17] or photovoltaic plants 56 [18], and loads, such as arc furnaces and cycloconverters 57 [19], [20], [21]. 58 The detection and measurement of power system subhar-59 monics are covered by international standards [22], [23], which 60 define the measurement methods, time frames, and indices. 61 For the evaluation of subharmonics, as well as harmonics 62 and interharmonics, the discrete Fourier transform (DFT) 63 performed with a rectangular window is one of the processing 64 tools recommended by the standard [22], which indicates 65 as basic measurement time frame an interval equal to ten 66 cycles (12 cycles) for 50-Hz (60-Hz) systems. Considering 67 power systems operating at 50 Hz, frequency variations over 68 time can occur, leading to variable time frames that are not 69 always equal to 200 ms. In the following, this article will 70 refer to the specific case in which the power frequency is 71 constant and fixed to 50 Hz. This restriction is intended to 72 simplify the analysis by avoiding the error contribution due to 73 the algorithm for power frequency estimation. However, the 74 presented results hold true regardless of the specific case that 75 is taken into account, as long as the additional error of the 76 power frequency synchronization algorithm with the network 77 frequency is considered.     [9]. Without loss of generality, this article will refer to 138 50-Hz power systems; very similar results can be obtained for 139 60-Hz power systems by changing the involved frequencies 140 and the duration of the time frame chosen for the analysis 141 of the waveforms. Thus, with particular reference to a 50-Hz 142 constant power system, the standard [22] suggests using the 143 DFT on time frames of 200 ms, resulting in a fixed frequency 144 resolution equal to 5 Hz, for the measurement of harmonic 145 and interharmonic components.

146
Since the frequencies of interest in this work are in the 147 range ]0, 50[ Hz, the measurement indices used to quantify 148 the interharmonic components at frequencies lower than 50 Hz 149 are the interharmonic group Y g and the gapless interharmonic 150 centered subgroup Y csg [22], as illustrated in Fig. 1 and defined 151 as in (1) and (2) considering the case of h = 0 where Y g is the Root Mean Square (RMS) value of all the 155 interharmonic components in the frequency interval between 156 two consecutive harmonic frequencies; Y csg is the RMS value 157 of the interharmonic group excluding the interharmonic com-158 ponents adjacent to the harmonics; V 2 h· f 1 +m·r is the RMS value 159 of the voltage at (h· f 1 + m · r ) frequency; f 1 is the power 160 frequency; and r is the frequency resolution equal to 5 Hz.

161
The conventional indices used to evaluate the ITs accuracy 162 and assign the accuracy class are the ratio and phase errors 163 defined at power frequency [26], [27]. In this work, the defin-164 ition of ratio and phase errors has been extended, considering 165 the indices in (1) and (2). The IT-PI is defined as follows:  inaccurate results due to the spectral leakage [28], [29], [30],

178
[31], [32]. In fact, in these cases, since the periodicity of This section aims at quantifying the error introduced by the 206 signal processing suggested by [22] for the measurement of 207 Y g and Y csg when subharmonics with frequencies in the range 208 [0. 1, 49.9] Hz are present in the analyzed signal.

209
For this purpose, two different simulations are performed. 210 In the first step, only subharmonic components in the range 211 [5, 45] Hz are considered, whereas, in the second step, also, 212 the subharmonics outside this frequency range are included in 213 the analysis. It is worth highlighting that the first step of the 214 analysis focuses on the first interharmonic group defined by 215 [22]. Additional tones, in the ranges ]0, 5[ and ]45, 50[ Hz, 216 adjacent to the first interharmonic group, are included in 217 the second step. As a result of the mismatch between the 218 periods of these components and the time frame used for the 219 analysis, they can introduce spectral leakage into the [5, 45] Hz 220 frequency range.

221
The PIs used for this analysis are the same introduced in 222 Section II for the IT [see (3) and (4)]. In particular, ε η is 223 obtained by assuming the following.   3) Y η,s is equal to the value calculated by implementing the 229 measurement method indicated by the standard [22].

231
In the first case, a voltage signal composed of a fundamental 232 tone plus one subharmonic, as described in (5), is numerically 233 simulated The fundamental tone has amplitude A f equal to 1 V, 236 and the frequency f 0 is fixed to 50 Hz; in this way, using 237 a sampling frequency equal to an integer multiple of the 238 signal frequency, there is no need for a specific technique 239 to estimate the signal frequency. Therefore, there is perfect 240 synchronization between the fundamental tone and the 200-ms 241 time frame, avoiding the spectral leakage contribution due to 242 the fundamental component. The subharmonic has amplitude 243 A sub−h equal to 1% of A f , frequency f sub−h variable in the 244 range [5, 45] Hz with a frequency step equal to 0.25 Hz, 245 and initial phase angle ϕ sub−h randomly (uniform distribution) 246 variable in the range [−π, π]. The signals are numerically 247 generated for a time duration of 10 s, and 100 initial phase 248 angles ϕ sub−h are extracted for each subharmonic frequency. 249 All the results reported in the following refer to the maximum 250 errors obtained by using the random variation of the initial 251 phase.

252
The simulation outputs are provided in Figs. 3 and 4 where 253 the mean absolute values of ε g and ε csg evaluated over 10 s are 254 reported along with their maximum values ξ g and ξ csg . As a 255 general comment, it can be observed that signal processing has 256 a slightly lower impact on the evaluation of Y csg compared to 257 Y g , being the maximum ξ g greater than the maximum ξ csg . This 258 is explained by considering that, in the evaluation of Y csg , the 259 tones at 5 and 45 Hz, introduced by the spectral leakage when 260 the analyzed time frame is not an integer multiple of the signal 261 Mean absolute value and maximum absolute value (ξ g ) of ε g , introduced by the signal processing in the measurement of Y g , versus the generated subharmonic frequency. period, are not included, and for this reason, the overall error is 262 reduced. The maximum ξ g is equal to 7.3%, and it is observed 263 for f sub−h equal to 6 Hz, whereas the maximum ξ csg is 6.9% The fundamental tone has amplitude A f equal to 1 V  second subharmonic has amplitude A sub−h,out equal to 1% of 289 A f , frequency f sub−h,out variable in the ranges [0.1, 4.9] and 290 [45.1, 49.9] Hz, and initial phase angle ϕ sub−h,out randomly 291 (uniform distribution) variable in the range [−π, π]. The 292 signals are numerically generated for a time duration of 10 s, 293 and 100 initial phase angles ϕ sub−h and ϕ sub−h,out are extracted 294 for each subharmonic frequency. Also, in this case, all the 295 reported results refer to the maximum errors obtained by using 296 the random variation of the initial phase. For sake of brevity, 297 only results related to ε g at f sub−h equal to 5, 22, and 45 Hz 298 are provided, but similar considerations also apply to ε csg and 299 different f sub−h frequencies.

300
As it can be observed in Figs where 341 k r = V p,r /V s,r rated transformation ratio (V p,r and V s,r are the rated primary and secondary voltages); RMS values of the primary and secondary harmonic voltages at frequency f sub−h ; phase angles of the primary and secondary harmonic voltage phasors at f sub−h .

342
Starting from this information, several scenarios are con-  In analogy to Section III-A, even with the presence of a 371 simulated IT, the case of a single subharmonic is first ana-372 lyzed. Here, all the possible combinations of: 1) IT frequency 373 response according to Table I and 2) frequency and phase of 374 the subharmonic inside the range [5, 45] Hz, according to 375 (5), are considered. The IT error contributions are evaluated 376 according to the IT-PI (4) introduced in Section II.

377
The main outcomes of this simulation are listed in the 378 following and summarized in Table II.

379
As a first result, it is evidenced that, for f sub−h integer 380 multiple of 5 Hz and for any combination of the IT ratio and 381 phase error, the PI ε g and ε csg assume the same values of the 382 IT ratio error at f sub−h with a constant time behavior.

383
For ϕ(0.1 Hz) equal to 0 rad and any value of ε(0.1 Hz), 384 the indices ε g and ε csg do not oscillate over time, and they are 385 overlapped with the IT ratio errors.

386
On the contrary, for ϕ(0.1 Hz) different from 0 rad, the 387 indices ε g and ε csg assume mean values equal to the IT ratio 388 errors but show an oscillating time behavior with a maximum 389 absolute value up to seven times the IT ratio error.

390
For sake of clarity, Figs. 8 and 9 show, respectively, ξ g and 391 ξ csg resulting from these simulations only in some specific 392 conditions listed in the following.    In analogy to Section III-B, the case of multiple subharmon-405 ics is then analyzed. Here, all the possible combinations of: 1) 406 IT frequency response according to Table I  For sake of clarity, the results are presented in three steps. 412 In the first step, the analysis is carried out in the following 413 conditions. 414 ξ g = ξ csg = ε g = ε csg = ε(15 Hz) Due to the presence of such a subharmonic tone, the signals 434 considered in this step have a periodicity that is not an integer 435 submultiple of the 200-ms analyzed time frame. This fact leads 436 ε g and ε csg to oscillate and have a mean value different from 437 ε(15 Hz). In other words, (9) does not apply anymore.

438
Figs. 10 and 11 show, respectively, ξ g and ξ csg for the three 439 simulated ITs (see Table III); they also show the absolute value 440 of the IT ratio error |ε(15 Hz)| = 0.7%, equal for all the three 441 simulated ITs.   2) ξ g = 6.3% and ξ csg = 4.6% for IT B .

448
3) ξ g = 3.6% and ξ csg = 2.7% for IT C .  It can be noticed that ξ g and ξ csg also strongly depend on 450 the f sub−h,out values. By the comparison of Fig. 10(a) with 451 Fig. 10(b), and Fig. 11(a) with Fig. 11(b), it can be observed 452 that the maximum values of ξ g and ξ csg decrease between 70% 453 and 80% when subharmonics in the [45.1, 49.9] Hz range are 454 present instead of the subharmonics in the [0.1, 4.9] Hz range. 455 In fact, for instance, looking at Fig. 10(a) and (b), for the IT A , 456 the maximum values of ξ g are 21.8% and 3.2%, respectively. 457 Looking at Fig. 11(a) and (b), for the IT A , the maximum values 458 of ξ csg are 14.3% and 4.1%.

459
In general, we can observe the following. 460 1) For f sub−h,out < 5 Hz [see Fig. 10(a) and 11(a)], both ξ g 461 and ξ csg are greater than |ε(15 Hz)|, and moreover, ξ g is 462 greater than ξ csg . 463 2) Instead, for f sub−h,out > 45 Hz, ξ csg is always greater 464 than |ε(15 Hz)| [see Fig. 11(b)], whereas ξ g is lower 465 than |ε(15 Hz)| for some frequencies [see Fig. 10 Therefore, with a f sub−h,out < 5 Hz, the spectral leakages 472 at the primary and secondary sides of the IT significantly 473 differ among themselves, and this leads the errors ε g and ε csg 474 to increase. Instead, with a f sub−h,out > 45 Hz, the spectral 475 leakages at the primary and secondary sides of the IT are 476 very similar, and this leads the errors ε g and ε csg to decrease. 477 Moreover, since the components at f sub−h,out < 5 Hz 478 produce a more significant leakage in the first portion of 479 the [5, 45] Hz range, ξ csg is lower than ξ g because Y csg 480 does not include the 5-Hz tone. Similarly, the components at 481 f sub−h,out > 45 Hz has a stronger influence on the last portion 482 of [5, 45] Hz range and, for this reason, ξ csg is higher than ξ g . 483 In the second step, the analysis is carried out in the 484 following conditions. 485 1) f sub−h,out is fixed to 4.9 Hz. In fact, from the analysis 486 of the results of all the numerical simulations, the worst 487 case resulted in the combination of two subharmonics: 488 one with f sub−h = 6 Hz and one with f sub−h,out = 489 4.9 Hz. For sake of clarity, this particular condition is not 490 presented before, but it is considered in the following. 491 2) An IT having ϕ(0.1 Hz) = −π/4 rad and ε(0.1 Hz) = 492 −30% (−30% and −π/4 rad are the limits of [33] for 493 a class 0.5 IT) is considered. As in the previous point, 494 this case produced the worst results. Again, for sake of 495 clarity, this particular condition is not presented before, 496 but it is considered in the following.  Fig. 12 shows the behavior of ξ g and the mean value of |ε g | 500 when f sub−h varies. The behavior of ξ csg and the mean value 501 of |ε csg | are not shown since they are lower than, respectively, 502 ξ g and the mean value of |ε g |.

503
As it can be observed, the maximum value of ξ g is equal 504 to 54.5%, and it is found when f sub−h is equal to 6 Hz.

505
In the third step, the analysis is carried out in the following 506 conditions. 507 1) f sub−h and f sub−h,out are fixed to, respectively, 6 and 508 4.9 Hz. This choice is made since, from the results of 509    Table I.   3) The amplitude of ξ g and ξ csg can dramatically increase 537 when the IT is supplied also with subharmonics in the 538 [0.1, 4.9] Hz frequency range. In this case, the observed 539 ξ g are always greater than ξ csg , and the maximum errors 540 are found for the combination of the tones at f sub−h 541 equal to 6 Hz and f sub−h,out equal to 4.9 Hz. Several commercial VTs were tested in order to quantify 548 the impact of VTs on the measurement of subharmonics and 549 give experimental evidence of the main results shown in 550 Section IV. However, for sake of brevity, in the following, 551 only the results related to two commercial VTs (one inductive 552 VT and one LPVT based on capacitive sensing technology) for 553 MV phase to ground measurement applications are shown.

554
The VTs' main features are summarized in Table IV. The 555 generation and measurement setup are shown in Fig. 14. 556 The reference voltage signal to be applied to the VTs under 557 test is provided by an Arbitrary Waveform Generator (AWG) 558 National Instrument (NI) PCI eXtension for Instrumentation 559 (PXI) 5422 (16 bit, variable output gain, ±12-V output range, 560 200-MHz maximum sampling rate, and 256-MB onboard 561 memory). The AWG generates a 4-MHz clock that is used 562 to derive the sampling clock; this allows obtaining coherent 563 sampling, thus avoiding spectral leakage. Acquisition of the 564 primary and secondary waveforms of the VT under test has 565 been performed through the data acquisition board PXIe-566 6124 (±10 V, 16 bit, and maximum sampling rate: 4 MHz). 567 time frames [34]. This test aims at providing the low-frequency 595 characterization of the transformer under test; in fact, the 596 obtained ratio and phase errors can be assumed as the reference 597 performance of the VTs under test when they are used to 598 measure voltage subharmonics in the frequency range [0.5, 599 49.5] Hz. In these tests, the following conditions apply: 1) 600 there is only one subharmonic tone and 2) the spectral analysis 601 is performed over a time frame that represents an integer 602 number of the signal period. This implies that the amplitude of 603 the single subharmonic tone is practically coincident with Y g 604 and Y csg , and so ε, ε g , and ε csg have the same value. As it can 605 be seen, the ratio and phase errors of the inductive VT under 606 test range from −0.4% at 0.5 Hz up to 0.1% at 49.5 Hz and 607 from 20 mrad at 0.5 Hz up to 4 mrad at 4 Hz, respectively, 608 so having a quite flat behavior, compared to its accuracy class 609 error limits. The ratio and phase errors of the LPVT under 610 test range from 9.7% at 0.5Hz up to 0.1% at 49.5Hz and from 611 338 mrad at 0.5 Hz up to −19.5 mrad at 15 Hz, respectively, 612 so having a worse behavior, with respect to its accuracy class 613 error limits.        It is worth noting that ξ g and ξ csg behave differently in the 643 two different frequency ranges, in accordance to the simulation 644 results discussed in Section IV.  Fig. 17(a) and (b)], whereas the following 651 holds. 652 1) ξ g ranges from 0.4% when f sub−h,out = 0.5 Hz down to 653 0.15% when f sub−h,out = 4.5 Hz [see Fig. 17(a)]. 654 2) ξ g ranges from 0.2% when f sub−h,out = 45.5 Hz up to 655 0.3% when f sub−h,out = 49.5 Hz [see Fig. 17 Fig. 17(b)].

660
For the inductive VT under test, which has a quite flat ratio 661 and phase errors (compared to the limits of its accuracy class), 662 as shown in Fig. 15(a) and (b), the difference between ξ g and 663 ξ csg is negligible.

664
As a general comment on the experimental results, they 665 mainly show that there are cases in which the errors introduced 666 by a VT in the measurement of the first interharmonic group 667 (ξ g or ξ csg ) are equal to twice the errors of the same VT 668 obtained through the laboratory characterization procedure 669 (ratio error ε). This result is observed for all the tested VTs, 670 even if here only two VTs are presented for sake of brevity 671 and clarity. It is worthwhile noting that this result is here 672 observed for two VTs based on different operating principles 673 and different low-frequency responses. In fact, for the LPVT, 674 |ε(10 Hz)| is equal to 4%, whereas ξ g reaches 8.5%. In the 675 same test conditions, the inductive VT has |ε(10 Hz)| equal 676 to 0.2%, whereas ξ g reaches 0.4%.

677
These results imply that, with the signal processing sug-678 gested by [22], it is not possible to compensate for VT 679 errors by using the frequency response data measured dur-680 ing laboratory characterization. Instead, the use of different 681 DFT windows [30] or measurement techniques [31], [32] 682 that reduce or avoid spectral leakage would ensure that the 683 maximum VT error ξ g coincides with the ratio error |ε|. As a 684 result, in these cases, more accurate measurements of the 685 power system subharmonics could be obtained by correcting 686 for the VT ratio error at subharmonics frequency, which would 687 represent a systematic error.

689
This article has analyzed from a numerical and an experi-690 mental point of view the performance of VTs when used to 691 measure subharmonics in compliance with the international 692 standards IEC 61869 family and IEC 61000-4-7. 693 The main outcomes of the work can be summarized as 694 follows.  He is currently an Associate Professor with the 880 Department of Engineering, University of Campania 881 "Luigi Vanvitelli." He is the author or a coauthor of 882 more than 200 papers published in books, scientific 883 journals, and conference proceedings. His main sci-884 entific interests are related to the development of innovative methods, sensors, 885 and instrumentation for power system measurements, in particular, power 886 quality, calibration of instrument transformers, phasor measurement units, and 887 smart meters.

888
Dr. Luiso is a member of the IEEE Instrumentation and Measurement 889 Society.