A Nonlinear and Non-Stationary Signal Analysis for Accurate Power Quality Monitoring in Smart Grids

Transcription

1 A Nonlinear and Non-Stationary Signal Analyi for Accurate Power Quality Monitoring in Smart Grid Silvano Vergura*, Giulio Siracuano, Mario Carpentieri*, Giovanni Finocchio * Department of Electrical and Information Engineering, Technical Univerity of Bari, Italy, ilvano.vergura@poliba.it mario.carpentieri@poliba.it, Department of Electronic Engineering, Indutrial Chemitry and Engineering, Univerity of Meina, Italy giulioiracuano@gmail.com gfinocchio@unime.it Keyword: Power Quality Monitoring, Power ytem, Smart grid, Non-tationary ignal analyi, Hilbert-Huang tranform, Wavelet CWT DFT DG DWT EMD HHT HT IMF P P PV PMF PQ PMU PV SG ROI WA WT Abtract Nomenclature Continuou Wavelet Tranform Dicrete Fourier Tranform Ditributed Generator Dicrete Wavelet Tranform Empirical Mode Decompoition Hilbert-Huang Tranform Hilbert Tranform Intrinic Mode Function Mean Power for line with no photovoltaic plant Mean Power for line with photovoltaic plant ProtoMode Function Power Quality Phaor Meaurement Unit PhotoVoltaic Smart Grid Region of Interet Wavelet Analyi Wavelet Tranform The broad diffuion of renewable energy-baed technologie ha introduced everal open iue in the deign and operation of Smart Grid (SG). Recently, everal tudie have focued attention on the Power Quality (PQ) when Ditributed Generator (DG) connected to SG inject a large amount of power. Thi paper dicue the influence of PhotoVoltaic (PV) plant in real ditribution line. In particular, a numerical tool ha been developed in order to tudy the active power of ditribution line. The dataet derive from real meaured acquiition of ditribution line feeding reidential and commercial uer. The mathematical approach i baed on both the Wavelet Analyi (WA) and the Hilbert-Huang Tranform (HHT) in order to elect and iolate the different operation mode of the ditribution line. Numerical reult highlight that PV plant trongly affect the time-domain power ignal. A thi ignal i typically non tationary and nonlinear, the HHT-baed approach allow to fix power diturbance and anomalie. 1 Introduction The ue of advanced ignal proceing tool give new inight into the tudy of the dynamic of SG when the exitence of DG introduce power diturbance. In fact, a non-uniform patial ditribution of the electrical power give rie to multi-mode and intermittent non-tationary olicitation [1]. For example, for SG with high penetration of DG, a ignificant amount of conventional generation i replaced with ditributed PV reource with the reult of the lack of reactive power [2]. The reduced ytem inertia i another conequence of utilizing higher amount of PV generator [3, 4], which decline the overall power ytem tability [5], uch a during tranient period. The monitoring of power ytem ha been alway an important tak. The power diturbance can be oberved in everal mode depending on line parameter (uch a power fluxe, length of the line, low/medium/high voltage network, paive or active line, etc.). When unexpected fluctuation appear, they introduce anomalie in the correct operation of the ytem. For example, while a hort circuit manifet itelf a a high-frequency component [6], a load variation give rie to a low-frequency component [7]. Thee problem are even more important for active line, i.e. line which can either aborb either feed the active power. In recent year, a Wide Area Meaurement Sytem (WAMS) baed on Phaor Meaurement Unit (PMU) ha been implemented, which provide favourable opportunity to monitor the low-frequency ocillation. The Dicrete Fourier Tranform (DFT) wa ued to analye PMU data in SG, in order to detect and to iolate untable ocillation [8]. The application of DFT how advantage in term of implementation, execution and noie-reitance, on the other hand no information of non-tationary behaviour can be identified (indeed data are trongly non tationary). Here we analyed the power diturbance in an active line, deriving from the mimatche between generation and load. 1

2 We have invetigated the adoption of both the Wavelet Tranform WT [9] and the HHT [10] for the problem of the reliable PQ monitoring. WT and HHT have been utilized for the detection of non-tationary behaviour and recognition of anomaly pattern, pecifically on negative active power condition [2]. An efficient and accurate computational method baed on WT [11] ha been ued on ignal collected by PMU data from a ditribution line in two different cenario: (i) the power meaured in a line fed by large PV plant (monitored a in [12]) indicated a P PV (t) and (ii) without PV generator, indicated a P(t). The WT identifie the time evolution of the mode of the electrical power a well a the abence of the excitation. Further inight of line dynamic in SG, can be achieved by uing the HHT. In particular, computation baed on HHT were able to eparate the time domain trace related to the harmonic and the teady tate. The technique developed here goe beyond the tate of the art of SG monitoring, becaue it permit to detect and locate the irregular operating condition, which are currently not revealed during traditional grid monitoring. The paper i organized a follow: Section 2 introduce the wavelet analyi, Section 3 the HHT, Section 4 propoe reult obtained on real PMU data, the concluion in Section 5 end the paper. 2 Wavelet Tranform A wavelet-baed analyi allow to characterize a ignal in the time-frequency pace pointing out non-tationary behaviour. For thi reaon, the WT ha been widely propoed to analye the diturbance event in the power ytem and SG [7,13-21]. In detail, for a time-domain ignal x(t), the continuou wavelet tranform i a linear function W u, given by: 1 * t u Wu, x t dt (1) being and u the cale and tranlation parameter of the mother wavelet ψ(t) which define the wavelet family function a 1 t u u, t. We have ued the complex Morlet wavelet mother[9]: t u tu j f / f C B u, e e (2) fb with a Fourier pectrum of 2 2 f B f f C j 2 uf u, f e e, where f B and f C are two characteritic parameter and Ψ(f) = F{ψ(t)} i the Fourier tranform of ψ(t). For a given fixed dimenion N of the cale et, we adopted the method propoed in [11] to find the optimal cale et i i 1,..., for the WT. N 3 Hilbert-Huang Tranform HHT i a recently developed method which i proved to be a ueful tool for tudying the nonlinear behavior of time erie. Non-linear analye baed on HHT [22] are uccefully ued to extract time-varying ocillation characteritic. By mean of thi technique, complex et of nonlinear and nontationary data can be decompoed into a finite collection of individual characteritic ocillatory mode, named Intrinic Mode Function (IMF), through the Empirical Mode Decompoition (EMD). The IMF have well-defined intantaneou frequencie and are aumed to repreent the intrinic ocillatory mode embedded in the original ignal. Let u recall the key mathematical point of thi technique. HHT conit of two part: Hilbert Tranform (HT) and EMD. Given a time-domain function x t, it HT y(t)=h{x(t)} i defined a P x y t d (3) t where P i the Cauchy principal value. If z t i the analytical ignal aociated to x(t), it reult, for all t, i t, where At x 2 t y 2 t zt xt iyt Ate and t arctan y t are the intantaneou amplitude x t and the phae aociated to the ignal, repectively. The intantaneou frequency ω(t) i defined a the time derivative d t of φ(t), t, while the intantaneou power P(t) = dt A(t) 2 reflect how the power of the ignal x(t) varie with the time [10,23]. The HT compute the intantaneou power and frequency of a mono-component ignal. A generalization of the notion of uch an analytic ignal to a multi-component one i poible by uing the EMD method [23]. EMD i an adaptive and efficient method applied to decompoe non-linear and non-tationary ignal. It extract a erie of IMF from the analyzed ignal by mean of an iterative proce which i known a ifting. It can be ummarized a follow: (1) tarting from the original ignal x(t), et h t x t i 1,2,... i, extract the local minima and local maxima from hi t ; (2) interpolate the local minima and local maxima with a cubic pline to form upper and lower envelope, repectively; (3) obtain the mean of the upper and lower envelope mi t and ubtract it from hi t to determine a new ProtoMode Function (PMF) hi 1 t hi t m t. The above procedure i repeated until hi 1 t IMF and then c t h t atifie the ending criteria (pecified below) of an j, where j 1,2,... n i the j-th i1 IMF component from the data. An ocillating wave to be an IMF mut atify two condition: i) the number of maxima and minima and the number of zerocroing differ only by one and ii) the local average i zero. To preerve the natural amplitude variation of the ocillation, ifting mut be limited to the lowet number of mathematically permiible tep; in thi ene, the choice of a proper topping criterion i crucial. Thi method i iterated by removing each ocillating wave which meet the above 2

3 condition, until the negligible reidue ignal r(t) i not an IMF. If the n IMF component have been determined, the original ignal can be recontructed by uing the HT a n x t cj t r t (4) j1 The ignal can be recat in term of the Hilbert tranform a n x t Re z t Re Aj t exp i j t dt (5) j1 where the reidue r(t) i ignored. Eq.(5) can be een a a generalized form of the Fourier decompoition for the function x(t) where both amplitude A(t) and frequency ω(t) are function of time. Thi approach inure that the intantaneou amplitude and frequency of each component of the reulting ignal have a phyical meaning. 4 Reult and Dicuion 4.1 Decription of the ytem under tet The ytem under tet i a SG contituted by everal paive and active line located near Bari (Italy). Thee line feed both reidential and commercial uer. Each line aborb a peak mean power in the range [50 350] kw over a length which varie from 248 to 472 meter. For the aim of thi paper, we have choen two power line: a paive one with a peak power of about 50 kw and an active one of about 70 kw of aborbed power. Power meaurement have a ampling period of 10 minute and have been captured between September 2013 and February 2014 for a total of 154 day with 144 ample per day (154x144=22176 event recorded). PMU are located at the beginning of each line. Our data reveal a quota of 938 event with no available power information from the line. The paive line ha no PV plant, wherea the active line ha 18 grid-connected PV plant with a total rated peak power of about 108 kw. Due to the high DG penetration, the active line i particularly intereting, becaue it exhibit often negative value of the mean aborbed power (i.e. it inject energy into the grid). Both the line have important load variation during the day and the week. repect to the P(t) ignal. Such diverity i due to the fact that the line aborbing P(t) exhibit a power curve which ubtantially follow the different energy need during the day, while the line aborbing P PV (t) take into account the injected power by the DG. In fact, a reported in Fig 1(a), everal time the aborbed power by the electrical load i comparable with the produced one by the DG S and ometime i le. Thi lead to an abrupt variation of the mean active power of the line. In addition, P3 mode eem to be mainly related to eaonal event that caue a change of the energy demand and load curve of both power line. According to thi, our finding aim u to point out that the P3 mode i ubtantially invariant for the two ignal of interet, On the contrary, P2 mode appear to be aociated with the alternation between daytime and night-time profile of power requirement that are greatly emphaized by the preence of DG and can explain it larger amplitude if compared with no PV line. Such incremental effect in the P2 mode that an higher DG penetration impoe on the power ytem are central to tudy the ytem tability iue a a whole. In particular, we dicovered an unexpected and dramatic boot in the P2 mode of P PV (t), which i four-fold higher than that related to the line without PV power. Thi harmonic i invetigated in depth uing WT becaue it period i near with the operating range of PV generator ( 12h). The aim i the extraction of the time-frequency behaviour of each ocillation in order to tudy the non-tationary dynamic in SG. 4.2 Numerical reult Fig.1(a) how an excerpt from the time domain data of the mean active power ignal a captured in the two available cenario: line with no DG, P(t) (olid red line), and fed by large PV plant (monitored a in [12]), P PV (t) (olid black line), repectively. According to the PMU data, we depicted in the upper frame of the figure, the time event with no power (olid gray tar). In addition, a Region Of Interet (ROI) i defined indicating the anomaly detected in P PV (t). Fig. 1(b) include both the Fourier pectra of P(t) (olid red line) and P PV (t) (olid black line), repectively. It i intereting to put in evidence the different pectral amplitude of the main harmonic (f P1 =11.4μHz 24h -1, f P2 =23.3μHz 12h -1, f P3 =34.7μHz 8h -1 ). P1 i the main mode of the power dynamic of the two line (with and without PV generator).. A hown in Fig 1(b), the amplitude of P PV (t) i double with Fig. 1. (Colour online) (a) Excerpt from meaurement of mean active power ignal for a line with no DG <P(t)> (olid red line) and connected to DG <P PV (t)> (olid black line). A 3

4 ROI i defined indicating the anomaly detected in P PV (t) while the time event with no power are drawn (olid gray tar) at the top for convenience. (b) Fourier pectra of P(t) (olid red line) and P PV (t) (olid black line), repectively, with evidence of the different pectral amplitude of the main harmonic (f P1 =11.4μHz (1/24)h -1, f P2 =23.3μHz (1/12)h -1, f P3 =34.7μHz (1/8)h -1 ). Fig. 2 depict the time-frequency repreentation for P(t) (a) and P PV (t) (b), repectively. Our wavelet analyi baed on Morlet a the mother function (f B =30 and f C =1 [11]) aim u to better evaluate the intermittent behaviour of the P2 mode. In particular, in (b) we are able to oberve a telegraphic ignal appearing and diappearing which ugget an irregular active power aborption due to the PV power. The negative power injection are caued by the impact of the increaed penetration on power ytem and they need to be properly aeed. We performed the HHT on the ignal P PV (t) to extract the independent ocillation and to invetigate the P2 mode deeply. Once extracted by mean of HHT [24], we applied the previou Morlet wavelet and computed the Wavelet calogram to evaluate the dynamic. Fig. 3 how the accuracy of the eparation proce, revealing the time-frequency behaviour of the P2 mode a eparated uing EMD. It provide evidence of highly non-tationary behaviour of the P2 mode, a extracted from the ignal P PV (t). Note the trong temporal coherence between the occurrence of event wherein no power ha been meaured (olid white tar in the upper part of the Fig. 3) which follow the nearet local maxima of the P2 mode. Thi indicate a poible relationhip between the mot of the unexpected fault in the line and the nonlinear amplitude of thi diturbance. Thee remark validate the importance of the non-tationary and non-linear analyi in the tudy of the dynamic in SG. Fig. 3. (Colour online) Time-frequency domain plot of the P2 mode a extracted from P PV (t) uing HHT. Reult confirm the accurate extraction of the anomaly from the ignal time trace. Again, the time event with no power are drawn (olid white tar) on the upper part of the figure for convenience. 5 Concluion Fig. 2. (Colour online) (a) Time-frequency domain plot of P(t) and P PV (t) (b) a computed uing our WT-baed method [20], howing the three different mode a detected. Note the reliable identification of the anomaly (P2 mode) from the power ignal. Again, the time event with no power are drawn (olid white tar) on the upper part of (a) and (b), for convenience. The inner diverity in the characteritic of renewable energybaed ditributed generation technologie give rie to new technical challenge for SG. The chance to propoe an unupervied method able to ytematically explore and dicover irregular operating condition in typical ditribution network lead to a very challenging tak. Here, a combined Wavelet and HHT-baed analyi i propoed. It demontrate to be a valuable framework to invetigate the impact of DG penetration on the power quality in SG. Both teady tate and dynamic behaviour of ditribution line with and without PV plant contribution are tudied and compared to identify the effect of PV ytem on the power line. The reult of teady tate analyi reveal that increaing the amount of power due to the DG lead to larger fluctuation of the active power. Accurate modal eparation in time aimed u to oberve that ditribution line with relevant contribution of PV power exhibit greater power diturbance preceding the mot of failure. Our reult indicate that the peak to peak active power of a ditribution line increae a the ratio between DG power and the conventional one increae. With thi in mind, a computationally efficient method to tudy the 4

5 operation of SG ha been developed. The characteritic of the propoed method guarantee it application for tudying everal typical iue of power ytem. Specifically, thi procedure ha hown the ability to tudy non-tationary power ytem waveform and non-linear dynamical ignal. Acknowledgement The paper ha been written within the framework of the project RES NOVAE - Reti, Edifici, Strade - Nuovi Obiettivi Virtuoi per l Ambiente e l Energia. Thi project i upported by the Italian Univerity and Reearch National Minitry (MIUR) and competitivene program that Italy i developing to promote Smart Citie Communitie and Social Innovation. Acknowledgement are due alo for the reviewer which have given ueful uggetion to improve the paper. Reference [1] K. Koziy, G. Bei, J. Alakon, A low-cot powerquality meter with erie arc-fault detection capability for mart grid, IEEE Tran. on Power Delivery, Vol. 28, N. 3, pp (2013). [2] S. Eftekharnejad, V. Vittal, G. T. Heydt, B. Keel, J. 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