A Fully Informative Phasor Measurement Unit for Distribution Networks With Harmonic Distortion

We introduce a fully informative distribution network phasor measurement unit (FI-DPMU), that is capable of performing a simultaneous estimation of phasor dynamics and harmonic components. This is in contrast with current state-of-the-art devices, that only provide information about the fundamental component of voltages/currents—by discriminating or filtering-out their harmonic content. The FI-DPMU hence represents a significant economical solution, since it bypasses the need to deploy power quality analyzers to retrieve full information about the network. To validate the accuracy of the FI-DPMU, we performed a hardware-in-the-loop implementation to emulate a distribution network that is subject to abrupt frequency variations and high harmonic distortion. The tests demonstrate that the FI-DPMU satisfies the standards of distribution network phasor measurement units (DPMUs), providing a real-time fast Fourier transform (FFT) as additional feature. Experimental results show a comparison between FI-DPMU measurement data with the information provided by a commercial DPMU.

estimation, while the estimation of the harmonic spectrum 101 itself is not performed. For example, popular DPMU device 102 manufacturers, propose the implementation of an additional 103 parallel device, acting as a power quality analyzer (see 104 e.g., [22]) to retrieve full information, i.e., phasor and har-105 monic estimation. Then the use of aggregators is suggested 106 (e.g., [23]) to display data of phasor estimation and power 107 quality to the operator. On the other hand, at the backstage 108 of commercial developments, there are several remarkable 109 approaches reported in the literature concerning phasor and 110 harmonic estimation. For example, in [24], a phasor and 111 harmonic estimator is presented using a Taylor-Fourier trans-112 form, alongside a theoretical example that permits to evaluate 113 its performance. In [25], the authors propose a harmonic syn-114 chrophasor estimation with the purpose of compensating the 115 frequency response function of the instrument transformer. 116 Another relevant algorithm is presented in [20], where the 117 issue of phasor and harmonic estimation is addressed using 118 a Kalman filter bank according to every harmonic of interest. 119 Summarizing, the general shortcomings found in the current 120 literature are: (i) the use of purely theoretical algorithms that 121 have not been tested on real-time devices, which undermines 122 their commercial diffusion; (ii) the use of very particular har-123 monic signals for compensation purposes; and (iii) the use of 124 legacy algorithms such as Kalman filters, where the assump-125 tion of a constant frequency must be kept to avoid the use of a 126 Jacobian-based implementation, which yields only tangential 127 approximations of the actual signal trajectories. 128 In contrast with the state-of-the-art in both, commercial 129 devices and research literature, we propose a solution that 130 retrieves both, phasor information of the fundamental com-131 ponent and the harmonic contents. We called this solution 132 fully informative distribution network phasor measurement 133 unit (FI-DPMU). We hence show that there is no need to 134 increase the number of hardware devices to simultaneously 135 perform phasor and harmonic estimation, which is detri-136 mental for the underlying measurement and instrumenta-137 tion costs. The FI-DPMU implies an upgrade of the DPMU 138 algorithm, i.e., a software enhancement, to simultaneously 139 operate as a power quality analyzer. This upgrade transforms 140 the device into an economical solution for distribution net-141 works with a high number of power converter interfaces and 142 electronic loads, e.g., distributed renewable generation and 143 electric vehicles. To show the advantages of the FI-DPMU, 144 we use a hardware-in-the-loop implementation of a more 145 realistic distribution network, using a dSPACE acquisition 146 hardware. Then, we show that our estimated data satisfies the 147 required standard for DPMUs, i.e., IEC/IEEE 60255-118-1 148 (see [1], [26]), even under abrupt frequency variations and 149 considerable harmonic distortion. To illustrate the accuracy 150 and high performance of the FI-DPMU, the measurement 151 data is also compared with data provided by state-of-the-art 152 commercial DPMUs. It is shown how the FI-DPMU provides 153 full information by incorporating a real-time FFT, together 154 with extremely accurate phasor estimations.

157
The phasor estimation process consists in the identification 158 of parameters A, ω and φ of the following sinusoidal signal: (1)

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The proposed approach must be able to perform the esti- represents a solution of a second-order differential equation 169 of the form:

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(3) 179 whose time-domain solution can be obtained as

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where T s ∈ R + is the sample time and t k+1 = t k + T s .

196
Expression (5) can be rewritten using the shift-operator σ as 197 follows 1 : 199 1 From this point on, we deal only with discrete-time quantities, consequently there is no risk of ambiguity by relaxing the notation.
where operator σ acts on a discrete-time (sampled) vari-200 able v(t k ) as σ v(t k ) = v(t k + T s ). Notice that (6) is 201 a discrete-time system valid for any arbitrary initial con-202 dition. The phasor vector [x α , x β ] can be expressed in 203 polar form using the following transformation from αβto 204 dq-coordinates (see [28]), also called discrete-time inverse 205 Park transformation: cos(ωt (gps) ) − sin(ωt (gps) ) sin(ωt (gps) ) cos(ωt (gps) ) where t (gps) = kT s , k = 1, 2, 3, . . ., is the periodic timestamp 208 reference provided by a GPS device. Applying transforma-209 tion (7) to (6) yields: which implies that components x d and x q are constants. 212 In terms of phasor quantities, they represent the real and 213 imaginary components of a vector in the the complex plane, 214 which in polar form can be expressed as: where magnitude and phase angle can be identified from 217 traditional complex number analysis as A = x 2 d + x 2 q and 218 φ = arctan x q /x d . Note that t (gps) permits to synchronize 219 every DPMU device within the network, as they run indepen-220 dently from one another. This synchronization is crucial in 221 the case of signal parameters variations, as usual in real-life. 222 In the following section, we propose, based on this model, 223 a phasor estimation scheme with adaptive capabilities to deal 224 with signals subject to parameter variations.

226
In the following sections, we propose the construction of 227 an adaptive estimator based on model (6), where a variable 228 angular frequency ω is considered instead, i.e., Based on model (9), the following estimator is proposed, 233 which involves an additional correction component and an 234 integral-like equation to ensure angular frequency estimation: 235 wherex α ,x β andω are the estimated variables; and γ and 238 ε are tunable adaptation gains. Notice that the feedback 239 VOLUME 10, 2022 (i.e., v = x α ).

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Remark 1: We follow a similar analysis to the one pro-251 posed in [28] (1). 256 The estimate of the fundamental component phasor, in its 257 polar form (according to (8)), is given by The following section presents a method for simultaneous 261 estimation of harmonics in the reference signal, which repre-262 sents an extension of the above adaptive phasor estimator.

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One of the main benefits of the present approach is its mod-265 ularity, which allows its extension towards the estimation of 266 harmonic components. For this, consider that the measured 267 signal y is distorted and has a Fourier series representation 268 comprising a fundamental component plus higher-order odd 269 harmonics (typically present in a distribution network), i.e., Notice that this description naturally involves the extension of consists in reformulating (10) as follows: where the estimation of the n-th harmonic of interest 280 (n ∈ {3, 5, 7, . . .}) is performed according to where γ , ε and ε n (n ∈ {3, 5, 7, . . .}) are tunable adaptation 284 gains.

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The proposed harmonic estimation extension has two ben-286 efits. First, it deals with the harmonic distortion that typi-287 cally undermines an accurate fundamental component phasor 288 estimation. Hence, it is no longer necessary to implement 289 low-pass filters nor lead compensators to clean-up the signal, 290 as the fundamental component phasor is estimated by the 291 algorithm without error nor delay. Second, a power quality 292 analyzer functionality is implemented, that simultaneously 293 determines the parameters of the fundamental component 294 (phasor estimation) and the harmonic components (FFT anal-295 ysis). The capabilities of the proposed FI-DPMU and its 296 implementation is illustrated in Fig. 1a, which is compared 297 against a typical state-of-the-art commercial set-up shown in 298 Fig. 1b.

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Remark 2: Parameter tuning: The following explicit con-300 ditions to tune the estimator parameters (αβ components 301 and fundamental frequency) have been obtained following 302 the procedure described in [28]

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The IEEE 519 Std. [29] indicates that, if the signal is not  greater than 5%. To study this situation, in this test, the 348 reference signal v(t) has been distorted with harmonics 3, 349 5, 7; whose amplitudes are fixed to 20%, 16% and 12% 350 of the fundamental, respectively. These harmonics suddenly 351 enabled at time 0.1 s to exhibit the transient. Fig. 5 shows 352 the time response of the FI-DPMU. Note that, despite the 353 harmonic distortion appearing in v(t), the αβ signals from 354 the estimator achieve, after few cycles, an almost sinusoidal 355 waveform. That is, the FI-DPMU estimates the parameters 356 of the fundamental component while alleviating the effect 357 of harmonic distortion. Moreover, as above mentioned, the 358 algorithm is able to simultaneously work as a power quality 359 analyzer providing an estimate of the harmonics magnitude 360 as shown in Fig. 6.

B. PHASOR AND HARMONIC ESTIMATION IN A NETWORK 392
This set of tests was prepared to further evaluate the per-393 formance of the simultaneous phasor and harmonic esti-394 mation capability of the proposed FI-DPMU in a network 395 application. For this, we consider to use the FI-DPMU as a 396 monitoring device in the single-phase microgrid shown in 397 Fig. 13, where the measuring points are indicated by J 1 , 398 J 6 and J 7 . This microgrid is emulated using the dSPACE 399 digital board and Simulink. The resistances, inductances and 400 capacitances per unit length of the distribution line are given 401 by R = 0.2 /km, L = 0.004 H/km and C = 5.7 mF/km. The 402 fundamental frequency is 60 Hz and the internal impedance 403 of the external network and DGs are 0.5+j0.43 and 404 1+j0.86 , respectively. Loads 1 to 3 are all 100+j0.01 , 405 while load 4 is 200+j0.01 . Additionally, we compare the 406 estimations coming from the FI-DPMU with the measure-407 ment of in-situ commercial DPMUs. The network frequency is equal to f = 60 Hz, the voltage 411 amplitude of the sources is 110 V. Furthermore, the DG1 412 associated to J 1 and DG2 associated to J 7 , have been per-413 turbed with the 3rd, 5th and 7th harmonics, whose ampli-414 tudes, as percentage (%) of the fundamental voltage, are set to 415 VOLUME 10, 2022  affect the phasor estimation response of the FI-DPMU. 433 We emphasize that even though both, the commercial DPMU 434 and the FI-DPMU, are able to accurately estimate phasors, 435 only the FI-DPMU is able to additionally provide harmonic 436 estimation. In this test, the DG2 frequency varies linearly from 58 Hz 441 to 62 Hz at the rate of ±1 Hz/s, as described in the stan-442 dard IEC/IEEE 60255-118-1 [26]. Moreover, as in the pre-443 vious tests, the DG1 and DG2 have been perturbed with the 444  3rd, 5th and 7th harmonics, whose amplitudes, as percent- despite of such a disturbance, both algorithms are able to 454 accurately estimate the frequency. Fig. 18 and Fig. 19 show, 455 a comparison of the voltage and current phasors at each 456 measurement point between the commercial device and the 457 FI-DPMU. The accuracy of the estimation is corroborated by 458 the computation of the TVE in Fig. 20. 460 We presented a fully-informative DPMU (FI-DPMU) for 461 the simultaneous estimation of phasor dynamics and har-462 monic contents. The proposed FI-DPMU exhibits all-in-463 one capabilities with respect to the current state-of-the-art 464 and commercial devices. The FI-DPMU was tested using a 465 hardware-in-the-loop implementation showing its adaptive 466 capabilities to abrupt parametric changes on the network 467 signal parameters. The state estimation was compared with 468 measurements provided by commercial DPMUs. The results 469 corroborated the high accuracy of the estimation, which was 470 measured according to the IEC/IEEE 60255-118-1 standard. 471 Computations were reduced to basic arithmetic operations, 472 which can be easily implemented using low-cost micro-473 controllers, e.g., the C2000 family [30]. In terms of practical 474 implementations, the aforementioned technical characteris-475 tics of the FI-DPMU result in a low-cost device that facilitates 476 the diffusion of DPMU technology and its rapid deployment 477 over modern distribution network. In terms of applications, 478 the proposed FI-DPMU provides data to alleviate not only 479 current state-of-the-art and legacy problems in distribution 480 network such as state estimation, fault detection, phase identi-481 fication, data-driven modeling, etc.; but also enables emerg-482 ing applications that up to now could be performed using a 483 single device such as e.g., harmonic responsibility sharing 484 assessment (see e.g. [31], [32], and [33]). In the latter case, 485 FI-DPMUs are capable to simultaneously retrieve informa-486 tion of the power injection contribution by distributed gen-487 eration in terms of phasor dynamics, and information about 488 the contribution of each source to the harmonic distortion 489 within the network. This emerging capability fosters also 490 the propagation of asynchronous renewable generation by 491 endowing the operator with the capability to fully assess the 492 impact of distributed resources in real-time.

493
Finally, we conclude that, since the core algorithm that per-494 mits simultaneous phasor and harmonic estimation is based 495 on the solution of standard discrete-time equations, it is a 496 straightforward matter to include yet more equations to the 497 algorithm. This was illustrated when adding the harmonic 498 estimation capability, which can arbitrarily accommodate any 499 number of harmonics of interest. Hence, such algorithmic 500 flexibility can accommodate further discrete-time algorithms 501 within the device and then provide important local infor-502 mation, e.g., island detection. Beside, it is worth noticing 503 that one of the most compelling features of DPMUs is their 504 capability to act in a synchronized coordinated way, since 505 there is an additional value of retrieving information in a 506 collective way, by mapping a relevant part of the network or 507 even the whole distribution circuit. Consequently, although 508