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Electric Power Systems Research 107 (2014) 175– 182

Contents lists available at ScienceDirect

Electric Power Systems Research

jou rn al hom e page: www.elsev ier .com/ locate /epsr

orphological filter applied in a wireless deadbeat control schemeithin the context of smart grids

.F. Costaa,∗, A.J. Sguarezi Filhob, C.E. Capovillab, I.R.S. Casellab

Universidade Federal da Bahia – UFBA, Salvador, BrazilUniversidade Federal do ABC – UFABC, Santo Andr′e, Brazil

r t i c l e i n f o

rticle history:eceived 17 May 2013eceived in revised form9 September 2013ccepted 21 September 2013

a b s t r a c t

This paper proposes a digital morphological filter to be applied on reference signals for a deadbeat controlof a doubly fed induction generator. The signals are wireless-transmitted from a remote operation centerand prone to be corrupted by spikes caused by a wireless fading channel. The proposed technique filteringand the control scheme are to be implemented in a microprocessor locally placed at the generator site. Thefilter acts on the signals at the receiving end of the channel and its outputs serves as clean references tothe deadbeat control. In order to evaluate the filter performance, corrupted signals have been generated

eywords:athematical morphologyFIGower controlind energyireless communication

by means of a simulated channel linking the remote center and the induction generator. The results showthe method is efficient in filtering out the spikes without provoking excessive delays.

© 2013 Elsevier B.V. All rights reserved.

mart grids

. Introduction

In recent times, renewable energy sources have been the recip-ents of increasing attention from governments and researchersround the world. This interest can be explained by the growingoncern about to reduce CO2 emissions, and also by the search-ng of economical alternatives for traditional energy sources likeetrol or coal. These renewable alternative sources, like solar, tide,r wind energy are usually connected to the power grid both in theransmission and distribution levels. This brings up new technicalhallenges to monitor and control the energy produced by theseources. Within this context, the development of smart grids (SG)rocedures is becoming mandatory for utilities [1].

SGs are modernized electrical power grids. They rely on a muchore efficient use of generation, transmission, and distribution

nfrastructure turning the demand and supply of energy balanced

nd avoiding contingencies in the system [2,3]. Among the greatenefits brought by the advent of SGs technologies, it can be high-

ighted the arisen of enabling techniques for optimal management

∗ Corresponding author at: Rua Aristides Novis, n.02, Federac ão, Salvador, Brazil.el.: +55 71 3203 9760/9761; fax: +55 71 3203 9779.

E-mail addresses: fabiano.costa@ufabc.edu.br, ffcostabr@yahoo.com.brF.F. Costa), alfeu.sguarezi@ufabc.edu.br (A.J. Sguarezi Filho),arlos.capovilla@ufabc.edu.br (C.E. Capovilla), ivan.casella@ufabc.edu.brI.R.S. Casella).

378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.epsr.2013.09.016

of wind power. Recently, advances in wind power technology havegreatly improved system integration issues. However, there arestill some unsolved challenges for expanding its use. Its employ-ment entails undesirable fluctuations of generated power due tothe usual variations of the wind speed, that, if not compensatedin real time, can lead to frequency imbalance and disturbance inthe stability of the electrical system. Although SGs can minimizethis problem through an efficient demand response for load con-trol and dispatch of other generation resources, the use of variablespeed aerogenerators and its precise power control system are stillnecessary.

Among the aerogenerators, the doubly fed induction genera-tor (DFIG) is the most general employed in wind power systems[4], due to its interesting main characteristics as, for instance, theability to operate at variable speed and the capacity to control theactive and reactive power into four quadrants [5,6]. A precise powercontrol of the aerogenerators is essential to maximize the gener-ated power. The advances in wireless communications have madepossible implementation of low-cost and multifunctional wirelesssensors and communication modules in wind power plants [7] anddrive systems [8]. Fig. 1 shows the general scheme of an aerogener-ator controlled by a SG operator through a wireless communicationchannel.

Many modern communication systems are based on wire-less transmission [9–11]. It provides benefits such as low cost,high speed links, and easy setup of connections among differ-ent devices/appliances. In literature, it is possible to find out

176 F.F. Costa et al. / Electric Power Systems Research 107 (2014) 175– 182

ol sch

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Fig. 1. Wireless system contr

ew researches referencing the application of wireless technol-gy for renewable energy systems [12,13]. However, wirelessransmissions are subject to distortions and errors caused by theropagation channel that can cause severe problems to the con-rolled and monitored equipments and, thus, to the energy plant as

whole. These signals, due to the destructive effects of the wire-ess fading channel, still appear corrupted by spikes or impulsiveoises even with the employment of forward error correction (FEC)oding scheme [14]. Such problems are more critical from thosehat usually occurs in telecommunications systems, designed tooice and data transmissions, where small errors can be detected,riggering requests for retransmission (generating delays) or even,n some cases, be ignored without any significant impact to theetwork.

The most common technique for noise suppression is low-ass filtering with a linear operator [15–17]. Unfortunately, this

s not appropriate for suppressing impulsive references. There arelternative linear methods as wavelets algorithms [18,19] and non-inear methods as median filtering [20] or stack filtering [21] thatan present better performance. In this paper, it is proposed thepplication of a morphological algorithm to filter out the spikesorrupting the references signals. This filtering procedure, referreds Feedback Windowed Denoising Morphological Filter (FWDMF),s based on the mathematical morphology theory [22,23], where

non-linear approach can take advantage of a priori knowledgef the time domain shape of the analyzed signals and the inter-erences corrupting them. One of the advantages of mathematical

orphology over other approaches is its intrinsically easiness of

ematic for an aerogenerator.

implementation and computational efficiency as it only deals withsums, subtractions, and extractions of maximum and minimumvalues.

This paper is organized as follows: the second section brieflydescribes the fundamental equations for the DIFG and its controlstrategy. The third section presents the proposed wireless codedsystem and the wireless fading channel. The fourth section sum-marily outlines the basics of the morphological theory and its mainoperators; the fifth one proposes the filter algorithm used in thisresearch. The results and discussions are presented in the sixthsection, and the last section concludes the work.

2. Machine model and deadbeat power control

2.1. Machine model

To begin with, let us settle the notation used throughout thissection. Thus, the subscripts 1 and 2 refer to physical values fromthe stator and rotor respectively. The subscript d and q apply to thesynchronous axes in which the currents i and voltages v vectorsare decomposed. L1, L2 and the proper inductances of the statorand rotor windings, while Lm is the mutual inductance. �vdq is thevoltage synchronous vector.

The DFIG power control aims independent stator active P andreactive Q power control by means of the rotor current regulation.For this purpose, P and Q are represented as functions of each rotorcurrent. Considering the stator flux oriented control that decouples

F.F. Costa et al. / Electric Power Systems

d

i

i

w

P

Q

pa

P

Q

w

acdt

2

apstb

Fig. 2. Deadbeat power control block diagram.

q axis, the equations relating stator and rotor current are [24,25]:

1d = �1

L1− LM

L1i2d (1)

1q = − LM

L1i2q, (2)

here �1 = �1d = |��1dq| is the magnitude of the stator flux.The active and reactive power are computed by:

= 32

(v1di1d + v1qi1q) (3)

= 32

(v1qi1d − v1di1q) (4)

The active and reactive powers in Eqs. (3) and (4) can be com-uted by using Eqs. (1) and (2), when the stator flux position is used,s:

= −32

v1LM

L1i2q (5)

= 32

v1

(�1

L1− LM

L1i2d

), (6)

here v1 = v1q = |�v1dq|.Thus, the rotor currents reflect on stator currents and on stator

ctive and reactive power by using stator flux position. This prin-iple can be applied on stator active and reactive power control byriving the rotor current of the DFIG with stator directly connectedo the grid supply.

.2. Deadbeat power control

Through the deadbeat control, the voltages are computed to bepplied on the DFIG in order to assure that the active and reactive

ower reach their desired reference values. The sample time is theame as the time of PWM modulator. A detailed controller descrip-ion and results can be seen in [25]. The Deadbeat power controllock diagram is shown in Fig. 2.

Research 107 (2014) 175– 182 177

The discrete samples of the rotor voltages, which are calculatedto guarantee null steady state error [25], are obtained by:

v2d[n] = �L2i2d[n] − i2d[n − 1]

T+ R2i2d[n − 1] − L2ωsli2q[n − 1]

− LMωsli1q[n − 1] (7)

v2q[n] = �L2i2q[n] − i2q[n − 1]

T+ R2i2q[n − 1] + L2ωsli2d[n − 1]

+ LMωsli1d[n − 1] (8)

For the active power control, the rotor current reference by usingEq. (5) is given by:

i2q[n] = i2qref= −2PrefL1

3v1LM, (9)

and for the reactive power control by using Eq. (6) is:

i2d[n] = i2dref= −2QrefL1

3v1LM+ �1

LM, (10)

where Pref and Qref are the active and reactive power referencessignals received by the wireless channel and filtered by the mor-phological filter. Thus, if the d and q axis voltage components arecalculated according Eqs. (7)–(10) and then, they are applied tothe generator, the active and reactive power convergence to theirrespective commanded values will occur. The desired rotor voltagein the rotor reference frame (ıs − ır) generates switching signalsfor the rotor side using either space vector modulation.

Stator currents and voltages, rotor speed and currents are mea-sured to stator flux position ıs and magnitude �1, synchronousfrequency ω1 and slip frequency ωsl estimation.

3. Wireless communication system

The wireless communication system, shown in Fig. 1, is respon-sible for transmitting the power control information to theaerogenerator. The system operates at 2.4 GHz with a bit rate of80.0 kbps (bit duration of 12.5 �s) and employs Quaternary PhaseShift Keying (QPSK) modulation and a Convolutional Coding (CC)scheme [26] based on a generator polynomial with constraintlength of 7 and code rate of 1/2 [27].

In order to evaluated the real impact of the wireless transmis-sion on the energy control system, a flat fading Rayleigh channelwith a Doppler spread of 180 Hz is considered. The modeling ofthe wireless channel includes the effect of multipath propagationand white noise. Assuming that the channel variations are slowenough that Intersymbol Interferences (ISI) can be neglected, thefading channel can be modeled as a sequence of zero-mean com-plex Gaussian random variables with autocorrelation function [28]:

Rh(�) = J0(2�fDTs) (11)

where: J0() is the zeroth order Bessel function, Ts is the signalingtime and fD is the Doppler spread.

In the receiving process, the complex low-pass equivalentdiscrete-time received signal can be represented by [29]:

r = � · s + n (12)

where: r = [ r(1) · · · r(Ns) ]T is the received signal vector, � =T

[ �(1) · · · �(Ns) ] is the channel complex coefficients vector, s =

[ s(1) · · · s(Ns) ]T is the transmitted symbol vector obtained afterbit interleaving, convolutional encoding and QPSK mapping, n =[ n(1) · · · n(Ns) ]T is the Additive White Gaussian Noise (AWGN)

1 ystems Research 107 (2014) 175– 182

vbp

ctaasb

4

1Ibd

y

wssao

y

a

w

ha

doie

se

y

asa

Ha

y

a

y

so

y

w

d11 d21

78 F.F. Costa et al. / Electric Power S

ector, and Ns is the number of transmitted coded control sym-ols. Note that the in Eq. (12), the dot · denotes a vector producterformed element by element.

Once recovered the transmitted vector s, assuming a perfecthannel estimation, the transmitted control bits can be retrievedhrough the operations of symbol demapping, code deinterleavingnd bit decoding. The retrieved bits can, then, be demultiplexednd converted into the power control signals. Finally, the powerignals can be applied to the morphological filter to be employedy the DFIG. The filter is described in the next section.

. Morphological filter

Mathematical morphology is a theory firstly developed in the960s to extract or enhance geometric features from digital images.

ts usage in signal processing retraces from the 1980s, [30]. Oneasic operation in the morphological theory is the dilation, ⊕,efined as:

[n] ⊕ g[n] = maxk

{y[n + k] + g[k]} (13)

here: y is the signal to be analyzed, and g is the of the so-calledtructuring element (SE). To better understand the operation, con-ider a signal y[n] and suppose that the SE g has two elements, g[1]nd g[2]. The discrete time positions 1 and 2 make the domain Dg

f g. The dilation of y through g is, then, provided by:

[n] ⊕ g[n] = max{y[n + 1] + g[1], y[n + 2] + g[2]}, (14)

The dilation output can be stored into a discrete signal w[n],ccording to:

[n + 2] = y[n] ⊕ g[n], (15)

ence, for instance, the first two elements of the dilated signal, w[n]re given by:

w[1] = max{y[0] + g[1], y[1] + g[2]}w[2] = max{y[1] + g[1], y[2] + g[2]}.

Observing Eq. (15), one notes that dilation output, w[n], isefined so as to ensure the operation is causal. This is mandatory inrder to use this operation in a real-time filtering scheme. If the SEs flat, for example, a vector of null elements, the dilation has theffect of swelling the signal y[n].

Another basic operation in the morphological theory is the ero-ion, denoted as �. Thus, a signal y[n] is eroded by a structuringlement g[n], accordingly to:

[n] � g[n] = mink

{y[n + k] − g[k]}, (16)

nd likewise the dilation, the outcome from the erosion can betored in a discrete signal w[n]. The erosion may be interpreteds a shrinking procedure on the signal y[n].

Other operators can be devised from the dilation and erosion.ence, the opening operator, denoted by the symbol ◦, is defineds:

[n] ◦ g[n] = (y[n] � g[n]) ⊕ g[n], (17)

nd the closing operator, denoted by •, is given by:

[n] • g[n] = (y[n] ⊕ g[n]) � g[n]. (18)

Within the context of noise suppression of electrocardiogramignals, the following morphological filter, involving the closing andpening operators, was proposed [31]:

f [n] = (y[n] ◦ g[n] • g[n] + y[n] • g[n] ◦ g[n])2

. (19)

This filter has the property of rejecting signal interferenceshich are shorter than the length of the SE g[n]. Here, this filter

Fig. 3. Windowing stage for proposed algorithm.

is denoted Denoising Morphological Filter (DMF). This paper pro-poses a slight modification of the DMF for purposes of denoising ofreference signals of a deadbeat controller. The performance of thefilter described in Eq. (19) hinges on the SE length and on the cor-relation between the structuring element and the analyzed signal.The faster the interferences to be filtered are in relation to SE, thebetter is the filter performance. On the other hand, setting a toolengthy SE imposes restrictive delays on the filter response.

5. Proposed filter algorithm (FWDMF)

The proposed filter aims to filter out spike interferences con-taminating dc reference signals. The first step to build up the filteris to select the SE. As the reference signals are values of active andreactive power, all SE elements equals null in order to adjust it asa flat vector. It is, therefore, completely correlated to the analyzedsignals. Its length is larger than the extension of the spikes, but atthe same time not be so large to impose unnecessary delay to thefilter response. As the spikes extensions are not certainly known apriori, the SE length must be set heuristically.

The proposed algorithm relies on a windowing scheme whichallows a real-time implementation of Eq. (19). Each operation iscarried out on a moving L-length window, where L is the SE length.Fig. 3 illustrates the windowing of the signal y[n] into a windowedsignal yj[n] before it can be eroded or dilated. The windowing boxhas its input signal a sample y[n] and output an L-vector yj .

Fig. 4 shows the block diagram scheme for filtering the referencesignals proposed in this paper. It reflects the Eq. (19), except for thewindowing feedback stage depicted at the bottom of the figure.This improves the filtering capability for denoising the analyzedsignal. The first term in Eq. (19) is the result of two operations, theopening and the closing executed in tandem. The left side of theblock diagram, in Fig. 4, illustrates the execution of these opera-tions. The proposed scheme, then, frames the samples y[n] into avector. The SE, next, erodes the windowed signal yj , producing thesample ye11[n], which in turn is windowed into a vector ye11. Thesame SE g, then, dilates this vector providing, as a result, the sampleyd11[n]. This sample is the result of the opening of the signal y bythe structuring element g. Afterwards, the scheme frames yd11 intoy which is dilated to y [n], and which, in turn, is windowed

into a vector yd21. This vector is eroded to give the sample yp1[n]. Asimilar process produces yp2, which is the second term of Eq. (19).These two terms are averaged, and the output yf [n] is fed back tothe first window yj .

F.F. Costa et al. / Electric Power Systems Research 107 (2014) 175– 182 179

6

isstc

pectet

e

3 3.2 3.4 3.6−200

200

Time (s)

Po

wer

(kW

)

Power referenceCorrupted power reference

Fig. 5. Wireless channel effect on reference power.

3 3.2 3.4 3.6−200

200

Time (s)P

ow

er (

kW)

Corrupted power referenceFiltered signal

Fig. 4. General scheme algorithm.

. Analysis of the simulation results

The power control system and the filtering algorithm have beenmplemented in the Matlab Simpower Systems. To carry out theimulation, the deadbeat power control strategy operates with aampling time of 5 × 10−5 s and the DFIG parameters are shown inhe Appendix. The active and reactive power references are stephanged.

As shown in Fig. 1, these references are the inputs of the wirelessower control. Fig. 5 shows the curves of the active power refer-nce to the deadbeat controller and the received reference afterorrupted by the wireless channel. From this Figure, it is observedhe severe noise interference imposed by the channel to the ref-

rence signal. Impulses occurring at random dominantly comprisehe interference.

A morphological filter is applied to the corrupted power refer-nce accordingly to the algorithm described in Section 5. The SE is

Fig. 6. Filtering on power reference.

a flat vector of null elements. Its extension covers more than theaverage duration of the spikes contaminating the signal. The SE cannot be too long, otherwise the filter response delays excessively. Inthis case, one selects a filter having the length L equal to 50 sam-ples. As the time step for the simulation is 50 �s, the SE lengthcorresponds to 2.5 ms. Fig. 6 depicts the filtered signal, in contrastto the noisy power reference. This figure shows a delay in the filterresponse each time there is a changing in the level reference. Thisdelay obviously relates to the SE length.

In order to illustrate this relation, Fig. 7 shows the speed of themorphological filter response for different L values. Hence, as theSE length decreases from 120 to 10, the filter response to the ref-erence is quicker. On the other hand, its capability to filter out theimpulsive noise is diminishes as expected. Fig. 8 illustrates this factas the filtering capacity for suppressing noise is satisfactory downto L equal to 50. For L equal to 30 and 10, spikes still pollutes thefiltered reference as one can note on the two lowest graphics on leftin the figure. For instance, between 3.0 and 3.2 s, there can be seenspikes contaminating the filtered signal when the SE length is 30.Fig. 9 also illustrates how the filter response velocity varies withrespect to the SE length. This figure shows a graphic relating the SElength to the time the filter response achieves 97% of the referencelevel.

One popular approach for filtering noisy signals is simply using awindow moving average. Fig. 10 shows this strategy for filtering thepower reference corrupted by the wireless channel. The simulationis carried out for two L filter lengths of 50 and 100 samples. It isevident the ineffectiveness of the method. Fig. 10 shows that evenwhen L doubles, the filtering does not properly filter out the spikeswhich tend to be less intensive in amplitude, however, larger intime than the ones contained in the original signal.

Fig. 11 shows the filtering of corrupted power signal referenceby the proposed algorithm with and without the procedure, making

a comparison of DMF and FWDMF methods. This figure elucidateshow the windowing feedback procedure, depicted in Fig. 4, canimprove the filtering capability of the filter proposed in [31]. The

180 F.F. Costa et al. / Electric Power Systems Research 107 (2014) 175– 182

2.7 3

−100

−50

2.7 3

−100

−50P

ow

er (

kW)

2.7 3

−100

−50

Time (s)

2.7 3

−100

−50

2.7 3

−100

−50

Po

wer

(kW

)

2.7 3

−100

0

Time (s)

ReferenceFilter response

ReferenceFilter response

ReferenceFilter response

ReferenceFilter response

ReferenceFilter response

ReferenceFilter response

L=120

L=100

L=70

L=50

L=30

L=10

Fig. 7. Filter response velocity for different SE values.

3 3.2 3.4 3.6−200

200

3 3.2 3.4 3.6−200

200

Po

wer

(kW

)

3 3.2 3.4 3.6−200

200

Time (s)

3 3.2 3.4 3.6−200

200

3 3.2 3.4 3.6−200

0

200P

ow

er (

kW)

3 3.2 3.4 3.6−200

200

L=120 L=50

L=100 L=30

L=10L=70

Fig. 8. Noise suppression on power refer

10 20 30 40 50 60 70 80 90 100 110 1200

0.02

0.04

0.06

0.08

0.1

0.12

SE length

Tim

e re

spo

nse

(s)

Fig. 9. Filter response time with respect to the SE length.

3 3.2 3.4 3.6−200

200

Time (s)

Po

wer

(kW

)

Corrupted power referenceWindow moving average filtering (L=50)Window moving average filtering (L=100)

Fig. 10. Window moving average for filtering the corrupted power reference.

Time (s)

ence signals for different SE values.

selected SE is a null vector of 50 elements. It is clear the betterperformance of the filtering when the algorithm aggregates thewindowing feedback. On the other hand, the feedback procedureimposes a larger delay for the filter response. This, in some cases,may be critical, for the controller performance. It is not case for thepresented application as shown in Fig. 12, where the signals pro-duced by the aerogenerator fairly follows the two references foractive and reactive power. It is worth stressing that the referencesignals are the ones resulted from the filtering of the control sig-nals corrupted by the wireless channel sent by the remote control

central.

Opposing to this situation, Fig. 13 shows the produced active andreactive power when there is no filtering process for the transmit-ted references. One notes that the control system tends to follow

3 3.1 3.2 3.3 3.4 3.5 3.6−150

−100

−50

−150

−100

−50

Time (s)

Po

wer

(kW

)

Power reference

Filter response (FWDMF)

Filter response (DMF)

Fig. 11. FWDMF and DMF filtering performance.

F.F. Costa et al. / Electric Power Systems

3 3.2 3.4 3.6−200

0

200

Time (s)

Po

wer

(kW

)

P

ow

er (

kvar

) Active power reference

Produced active power

Reactive power reference

Produced reactive power

Fig. 12. DFIG control performance.

3 3.2 3.4 3.6−200

0

200

Tempo (s)

Po

wer

(kW

)

3 3.2 3.4 3.6−300

0

300

Tempo (s)

Po

wer

(kv

ar) Produced reactive power

Produced active power

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[24] B.H. Chowdhury, S. Chellapilla, Double-fed induction generation control forvariable speed wind power generation, Electr. Power Syst. Res. 76 (9–10) (2006)786–800.

[25] A.J.S. Filho, E. Ruppert, A deadbeat active and reactive power control for doubly-

Fig. 13. DFIG control performance without the filtering procedure.

he spikes which contaminate the references. These ones can per-anently damage the aerogenerator, the wind generation system,

r even cause a loss of system efficiency since the machine willot generate its maximum power track at that moment, and addi-ionally, they generate undesirable harmonic components to theower grid. The damage related to wind generation occurs becauseigh values of di/dt can completely deteriorate the Insulated Gateipolar Transistors (IGBTs), and, consequently, through the poweronverter, can cause short circuits in rotor and/or stator of theenerator.

. Conclusions

This paper has introduced a filtering algorithm based on theathematical morphological theory for improving the robustness

f a deadbeat control system for a Double Fed Induction Genera-or (DFIG) with regards the destructive effects of a wireless fadinghannel. This application is increasingly relevant in a smart grid sce-ario. The proposed filter has been built by weaving the openingnd closing morphological operators together with a structuringlement (SE) vector composed by null elements. Here, the filter haseen designated Feedback Windowed Denoising Morphological Fil-er (FWDMF). It relies on a feedback windowing procedure whichnhances the performance of a previously proposed Denoisingorphological Filter (DMF). The SE shape turns the filter suitable

or filtering out impulsive noise from dc reference signals. Theesults show the proposed filtering technique properly filters outhe spikes caused by the wireless communication at the input of theFIG without introducing any significant delay that compromises

he system stability. Therefore, the physical integrity of the gener-tor and the power quality delivered to the power grid have beenuaranteed, showing the operational viability of wireless commu-

ication in this analyzed scenario.

Research 107 (2014) 175– 182 181

Acknowledgements

The authors would like to thank CNPq, CAPES, and FAPESP forthe funding of this research.

Appendix.

Doubly fed induction generator parameters [32]:R1 = 24.75 m�; R2 = 13.3 m�; LM = 14.25 mH; Ll1 = 284 �H;

Ll2 = 284 �H; J = 2.6 kg m2; NP = 2; PN = 149.2 kVA and VN = 575 V.

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