A Multiconductor Model of Power Line Communication in Medium-Voltage Lines

A icle A Mul iconduc o Model o Powe Line Communica ion in Medium-Vol age Lines Lesek F anek * and Pe Fiedle Facul y o Elec ical Enginee ing and Communica ion, B no Uni e si y o Technology, Technicka 3082/12, 616 00 B no, Czech Republic; [email p o ec ed].cz *Co espondence: [email p o ec ed].cz Academic Edi o : Ne ille R. Wa son Recei ed: 26 May 2017; Accep ed: 12 June 2017; Published: 15 June 2017 Abs ac : Mos powe line communica ion (PLC) models a e designed o da e simula e powe lines as wo-wi e lines. Howe e , in al e na ing cu en (AC) elec ical dis ibu ion, he wo-wi e op ion is seldom applied, and medium- ol age lines a e mos o en based on he h ee-phase con igu a ion. In his con ex , he in luence o he g ound, which cons i u es ano he conduc o wi h speci ic pa ame e s, canno be neglec ed. Two-wi e models a e cha ac e ized by limi ed accu acy, no allowing us o simula e ce ain majo phenomena a ec ing PLC. This, o example, could embody he answe o he ques ion o whe he i is mo e ad an ageous o ansmi a signal independen ly h ough each phase, e e ence he signal wi h espec o ano he phase o o use he g ound as a e e ence. This pape discusses a mul i-conduc o model ha elimina es he disad an ages ou lined abo e; he p oposed model exploi s he mul i-conduc o eleg aphe ’s equa ions. In o de o be able o include medium- ol age (MV)/ low- ol age (LV) ans o me s in medium- ol age ne wo k models, we cons i u ed a ans o me model. The designed models we e alida ed on a eal medium- ol age ne wo k. To be able o e alua e he sui abili y o he PLC, he noise in he medium ol age ne wo k was measu ed in o de o de e mine he signal- o-noise a io (SNR). Keywo ds: powe line communica ion; sma g ids, in e ne o hings; machine- o-machine communica ion 1. In oduc ion Powe line communica ion (PLC) has been used o almos a hund ed yea s o a ious pu poses wi hin a b oad ange o ields, including elephony [ 1 ], s ee ligh ing con ol, and in e coms [ 2 ]. A p esen , PLC inds wide applica ion in sma g ids. PLC echnologies could be s a i ied in o h ee ca ego ies [3]. The i s ca ego y, he ul a-na owband ype o communica ion, is e y slow and p esen mos ly wi hin legacy sys ems [ 4 ]. Ul a-na owband PLC in sma g ids is used mainly in he US in con igu a ions wi h only ew elec ici y me e s behind he ans o me , as his ype o PLC is able o c oss medium- ol age (MV)/ low- ol age (LV) ans o me s and each high ol age ans o me s [ 5 – 7 ]. Thus, he PLC ne wo k ex ends o e all LV ne wo k segmen s ha a e connec ed o he gi en MV ol age ne wo k. The second class con ains na owband communica ion, he mos common solu ion o sma g ids. This g oup includes a numbe o s anda ds and p op ie a y app oaches, which can be subdi ided in o communica ion wi h one ca ie equency and mul i-ca ie equencies [ 4 , 7 ]. The ange o a ailable equencies in di e en pa s o he wo ld is assigned by ele an egula o y bodies [ 8 ]. One o he mos popula s anda ds in his ca ego y is PRIME [9]. Ene gies 2017,10, 816; doi:10.3390/en10060816 www.mdpi.com/jou nal/ene gies Ene gies 2017,10, 816 2 o 16 The hi d ype, b oadband communica ion, exhibi s a high speed and limi ed communica ion ange, making i a ool mos o en employed o b idge he E he ne connec ion wi hin a single building. Howe e , applica ions o sma g ids a e a ailable oo [4,10]. Sma g ids embody he in oduc ion o in o ma ion and communica ions echnologies (ICT) in o he dis ibu ion ne wo k o acili a e cos educ ion, inc ease he powe supply quali y, and educe he nega i e aspec s ela ed o he impac o ene gy p oduc ion and dis ibu ion on he en i onmen . Wi hin he di e en ypes o communica ion used in sma g ids, PLC e y equen ly ensu es he bidi ec ional da a exchange be ween he elec ici y me e s and da a concen a o s loca ed a subs a ions [11]; om he subs a ions, he da a a e usually sen o se e s ia mobile ne wo ks. This pape is in ended o in oduce a model o PLC o e a h ee-phase medium- ol age al e na ing cu en (AC) g id. Mo eo e , aking ad an age o he de eloped model, he au ho s a emp o esol e he ques ion o whe he i could be possible o communica e be ween he ans o me s in a medium- ol age g id, and, i so, wha pa ame e s can be expec ed. 2. Mul i-Conduc o Powe Line Model The p oposed mul i-conduc o powe line model is based on he eleg aphe ’s equa ions o mul iconduc o lines; mo e de ailed in o ma ion on he gene al solu ion o he di e en ial equa ions o such lines can be ound in, o example, [ 12 , 13 ]. Ki chho ’s laws a e used o de i e he o mulas exp essing he ol age and cu en in he phaso o m o he elemen a y sec ion o he line, which is shown in Figu e 1: ∂V(z) ∂z=−(R+jωL)I(z), ∂I(z) ∂z=−(G+jωC)V(z), (1) whe e z deno es he posi ion a he conduc o . One o he conduc o s is iden i ied as he e e ence conduc o . The ma ix V ep esen s he ol age be ween he indi idual conduc o s’ nodes and he e e ence conduc o ’s node, ound a he z posi ion o a e e ence conduc o , and he ma ix I de ines he cu en s lowing h ough each o he conduc o s. Bo h o hese ma ices exhibi he size (n ; 1 ) . The ma ices R , L , G and C ha e he dimension (n ; n) , whe e n is he numbe o conduc o s wi hou he e e ence conduc o , and hey a e symme ical wi h espec o he diagonal. The esis ance, induc ance, conduc ance, and capaci ance a e speci ied as pe -uni -leng h pa ame e s. i* lii* gii* 0* j* ljj* gij*gjj*cij* cii* V V A A Vj0 Vi0 Ij0 Ii0 lij* z cjj* Figu e 1. Elemen a y sec ion o he line. The ma ix Rcan be exp essed as: R=" i+ 0 0 0 j+ 0#. (2) The sum o he esis ances o he app op ia e conduc o and e e ence conduc o is ound on he main diagonal, whe eas he esis ance o he e e ence conduc o is hen o -diagonal. Ene gies 2017,10, 816 3 o 16 The ma ix Lcan be w i en as: L="lii lij lij ljj#. (3) whe e he induc ances on he diagonal ep esen he induc ance be ween he ele an conduc o and he e e ence conduc o ; he mu ual induc ance o he wo ele an conduc o s is o -diagonal. The ma ix Gcan be exp essed as: G="gii +gij −gij −gij gjj +gij#. (4) whe e he sum o he conduc i i y be ween he ele an conduc o and all he o he conduc o s, including he e e ence conduc o , lies on he main diagonal. Ou side he main diagonal o he conduc i i y ma ix, he conduc i i y be ween he wo ele an conduc o s is ma ked wi h he minus sign. The ma ix Ccan be exp essed as: C="cii +cij −cij −cij cjj +cij#. (5) whe e he main diagonal con ains he sum o he capaci ances be ween he app op ia e conduc o and all o he o he conduc o s, including he e e ence one. Ou side he main diagonal, he capaci ance be ween he wo ele an conduc o s is ma ked wi h he minus sign. To simpli y he no a ion, he impedance and admi ance ma ices o he ansmission lines a e de ined as ollows: Z= (R+jωL), Y= (G+jωC).(6) Fo he second o de de i a i e o ol age acco ding o he line posi ion, we ha e: ∂2V(z) ∂z2=ZYV (z).(7) This is a sys em o n di e en ial equa ions wi h n unknowns; in o de o sol e i , we ha e o in oduce he subs i u ion: ZY =T"λ10 0λ2#T−1=TΛT−1. (8) whe e T is he eigen ec o o he ma ix ZY , and Λ deno es he ma ix ha has he eigen alues o he ma ix ZY on i s diagonal. By in oducing ano he subs i u ion, whe e: Vm=T−1V.(9) I is hen possible o ew i e Equa ion (7) as: ∂2V(z) ∂z2=ΛVm(z). (10) Now, we ha e ob ained nindependen di e en ial equa ions wi h one a iable. By in oducing he ma ix Γ: Γ=√Λ. (11) Ene gies 2017,10, 816 4 o 16 he gene al solu ion o hese equa ions can be ound in he o m: Vm(z) = e−ΓzV+ m+eΓzV− m. (12) No e ha he exponen unc ions in Equa ion (12) a e ma ix exponen s; an exponen ial o a ma ix ep esen s an in ini e Taylo se ies and can be compu ed aking ad an age o he expm() unc ion in compu e p og ams such as Ma lab. The cha ac e is ic impedance o he line hen equals: Z0=TΓ−1T−1Z. (13) The dependence o he ol age and cu en a he beginning o he line on he ol age and cu en a i s end can hus be exp essed as: Vin =Tcosh (Γl)T−1Vou +Tsinh (Γl)T−1Z0Iou , Iin =Z−1 0Tsinh (Γl)T−1Vou +Z−1Tcosh (Γl)T−1ZIou .(14) No e ha he hype bolic unc ions in Equa ion (14) a e ma ix hype bolic unc ions; in compu e p og ams, his can be compu ed using sinhm() and coshm() unc ions. 2.1. A Line Model o Mul iwi e T ansmission Lines Any ne wo k elemen can be desc ibed as a mul i-po ia he ma ix Mi: "Vin Iin #="AiBi CiDi#"Vou Iou #=Mi"Vou Iou #. (15) To ep esen a mul i-conduc o line as a mul i-po ma ix, we can use Equa ion (14), which is al eady a ailable in he equi ed o m. The load model can be exp essed as an admi ance ma ix, whose in e sion will p oduce an impedance ma ix. The admi ance ma ix can be w i en as: YL="Yii +Yij −Yij −Yij Yjj +Yij#. (16) whe e he diagonal con ains he sum o conduc i i ies be ween he co esponding conduc o and all o he conduc o s, including he e e ence one. The conduc i i y be ween he espec i e wo conduc o s is o -diagonal wi h a minus sign. The equency dependen ma ix H( ) o he ol age ans e s be ween he indi idual conduc o s can be de e mined using he load admi ance ma ix and a ma ix M , which comp ises he ma ices A , B,C,D, and is calcula ed as he p oduc o he ma ices Mio he indi idual mul i-po s. The ma ix H( )can be compu ed as ollows: H( ) = (A+BY L)−1. (17) Consequen ly, he powe line b anch ending wi h he load YL(a ans o me ) could be modeled as a mul ipo ha ep esen s he pa allel admi ance Yp . In o de o calcula e he Yp , i is necessa y o compu e he ma ix M o he line, whe e he M comp ises he ma ices A , B , C , D (as ou lined in Equa ions (14) and (15)). The esul ing admi ance o he whole b anch can hen be calcula ed as: Yp=IinV−1 in = (CV L+DIL)(AV L+BIL)−1 = (C+DY L)(A+BY L)−1.(18) Ene gies 2017,10, 816 5 o 16 The mul i-po pa allel admi ance can be ep esen ed by an Mi ma ix. Since he ou pu and inpu ol ages a e equal, he ma ix A is an iden i y ma ix, and he ma ix B embodies a ze o ma ix. The ma ix C hen equals he b anch admi ance ma ix Yp, and he ma ix Dis he iden i y ma ix. 3. Pa ame e s o he O e head Lines and Cables The p ocedu e cha ac e ized abo e can be employed o he modeling o o e head lines and cables as well; howe e , i is ei he necessa y o know he ma ices R,L,G,Co Zand Y. The in e nal esis ance o he line is equency dependen , and we de ine i as he ma ix Rc( ) , whose diagonal con ains he in e nal esis ances o he indi idual conduc o s, caused p ima ily by he esis i i y o he conduc o ma e ial, he skin e ec , and he empe a u e o he conduc o . The elemen s o he Rc( )can be exp essed as: cii = dkϑkAC. (19) whe e d is he esis ance o 1 m o he conduc o a 20 ◦ C wi hou he skin e ec , kϑ is he empe a u e coe icien o he conduc o ’s esis ance, and kAC is he esis ance coe icien esul ing om he skin e ec . 3.1. G ound Impedance G ound impedance was independen ly de ined by Ca son [ 14 ] and Pollaczek [ 15 ]. To e alua e hei impedance o mula, we need o sol e in eg al e ms whose analy ical in eg a ions a e impossible [ 16 ]. While he gi en in eg al could no be esol ed analy ically, a se ies o app oxima ions we e in oduced, and hese a e compa ed wi hin [ 17 ]; an app oxima ion using a loga i hmic unc ion is p esen ed in [18]. A e y p ecise solu ion o ou simula ions is achie able ia compu ing he Pollaczek-de i ed in eg al nume ically by he p ocedu e desc ibed in [ 16 ], whe e he au ho s de i e he g ound impedance o mula: ze(jω) = jωµ0 2πZπ 2 0 2e−H an(Φ) an(Φ) + q an2(Φ) + jωµeσe cos(x an(Φ)) cos2(Φ)dΦ.(20) whe e he H ep esen s he ele an heigh o he o e head conduc o o , al e na i ely, dep h o he unde g ound conduc o ; x ep esen s he mu ual conduc o ho izon al dis ances; µe is he co esponding ai /soil pe meabili y; and Φ is a ans o med in eg a ion a iable. All o he quan i ies a e desc ibed in mo e de ail wi hin [ 16 ]. The conduc i i y o he g ound σe is a ailable in specialized maps and a lases [ 19 ]; al e na i ely, i can be measu ed, o example, using he magne o ellu ics me hod [20]. 3.2. O e head Line Pa ame e s The nume ous me hods o he modeling o an o e head powe line a e discussed wi hin a la ge se o pape s, including [17,21,22]. To acili a e he ela ed calcula ions, he g ound should in a iably cons i u e he e e ence conduc o , ega dless o he ac ha ei he he g ound o ano he phase embody he e e ence o he communica ion. The impedance and admi ance o an o e head powe line can be exp essed as: Z=Rc( ) + Ze( ) + jωL, Y=jωC.(21) whe e Rc( ) is he in e nal esis ance o he indi idual conduc o s de ined as desc ibed abo e; Ze( ) is he g ound impedance cha ac e ized in Sec ion 3.1; L , de ined below, deno es he induc ance ma ix o Ene gies 2017,10, 816 6 o 16 an o e head powe line; and C , also de ined below, ep esen s he capaci ance ma ix o he o e head powe line. The induc ance ma ix elemen s can be calcula ed using he equa ion o he induc ance o a wi e o e a pe ec ly conduc ing su ace [16]: l=µ0 2πln D2 D1. (22) In he case o elemen s loca ed on he ma ix diagonal (deno ed lii), D1and D2a e: D1= i, D2=2hi.(23) whe e i is he adius o he ele an conduc o , and hi deno es he clea ance be ween he gi en conduc o and he g ound. In elemen s ou side he ma ix diagonal (deno ed lij), D1and D2a e exp essed as ollows: D1=q(hi−hj)2+x2 ij, D2=q(hi+hj)2+x2 ij. (24) whe e hi and hj deno e he conduc o - o-g ound dis ance, and xij is he ho izon al dis ance be ween he gi en conduc o s. The capaci ance o an o e head powe line can be de e mined using he o mula o conduc o s in a homogeneous en i onmen [21]: CL =LC =µ0ε01n⇒C=µ0ε0L−1.(25) whe e ε0 is he pe mi i i y and µ0 he pe meabili y o acuum. How o measu e line- o-g ound capaci ance is desc ibed in [23]. 3.3. Unde g ound Powe Lines (Cables) The shielding is conside ed he e e ence conduc o . This also applies whe e shielding is no used as a e e ence o he communica ion signal ansmission. I an unsc eened cable is used, he g ound can be ega ded as shielding wi h an in ini e adius. The ma ix R( ) cons i u es he sum o he abo e-de ined ma ices Rc , which ep esen he impedances o he indi idual cable conduc o s, and Rs , whose dimension is iden ical o ha o he ma ix Rc ; all elemen s o he ma ix Rs exhibi a alue equal o he in e nal esis ance o he shielding, acco ding o Equa ion (19). In an unsc eened conduc o , he ma ix Ze is u ilized ins ead o he Rs , as ou lined in Sec ion 3.1, whe e he conduc o - o-g ound clea ance equals c1−bi[17,24]. The induc ance ma ix could be de ined acco ding o [25] as: lii =µi 2πln c2 1−b2 i c1ai , lij =µi 4πln c4 1−bibj2−2bibjc2 1cos θij c2 1b2 i+b2 j−2bibjcos θij. (26) whe e µi is he absolu e magne ic pe meabili y o he in e nal insula ion. The meaning o he o he a iables is shown in Figu e 2. Ene gies 2017,10, 816 7 o 16 μ ε Θi,j ai bj aj bi c1 c2 i j Figu e 2. A diag am o a shielded cable [25]. The cable capaci ance can be de e mined om he o mula [21] as: CL =LC =µiεi1n⇒C=µiεiL−1.(27) whe e εi is he pe mi i i y o he in e nal insula ion, and µi deno es he absolu e magne ic pe meabili y o he in e nal insula ion. The ans e se conduc i i y o he cable is de inable, acco ding o he o mula p oposed in [ 26 ], as: G C=σi εi⇒G=Cσi εi .(28) whe e σi is he conduc i i y o he in e nal insula ion, and εi deno es he pe mi i i y o he in e nal insula ion. 4. T ans o me Model Se e al esea ch epo s, o example [ 27 ], p esen ans o me models, bu hey a e no sui able o a mul i-line PLC model. Since he communica ion in ypical PLC sys ems is no in ended o pass h ough a ans o me , ou ans o me is modelled jus as a load. Such an a chi ec u e co esponds o he equi emen s o he ypical MV/LV g ids ope a ed in he Eu opean Union. A model o a eal ans o me is shown in Figu e 3. The wi es a, b, c, n a e in oduced only o connec he load ep esen ing a low ol age ne wo k wi hou a ans o me . The model does no allow us o desc ibe he ansmission h ough he ans o me bu is sui able o desc ibing he ans o me as a mul i-line load. The pa ame e s o he gi en model we e ob ained ia measu emen s on a ans o me manu ac u ed by BEZ BRATISLAVA, ype T0326/22 10000/400(231) V 200 kVA (he ea e , we use he abb e ia ed code T0326/22). I he ans o me is symme ical and undamaged, he alues o he model elemen s indica ed in Figu e 3a e iden ical o all he phases. We hen ha e: R1=R4=R5=R6, L1=L4=L5=L6, C=C2=C3=C4, R2=R7=R8=R9, L2=L1=L2=L3, R3=R1=R2=R3. In Figu e 3, he poin s A , B , and C ep esen he phases on he medium- ol age side; G deno es he g ound on he medium- ol age side; a , b , c a e he phases on he low- ol age side; and n is a neu al Ene gies 2017,10, 816 8 o 16 conduc o o he g ound on he low- ol age side. The load o he low ol age side is ep esen ed by ZLV and is connec ed o he poin s an , bn , and cn . I is assumed ha he load is symme ical; he e o e, each node is loaded wi h he same impedance ZLV . To simpli y he no a ion, he impedances Z1,Z2,Z3can be in oduced: Z1=iωR1L1 R1+iωL1 , Z2=iωR2L2 R2+iωL2 +R3, Z3=1 iωC. (29) The impedance be ween a phase and he g ound is: ZLG =3Z1(Z2+ZLV)Z3+Z1Z2 3+ (Z2+ZLV)Z2 3 3Z1(Z2+ZLV ) + 3Z1Z3+3(Z2+ZLV )Z3 . (30) and he impedance be ween he phases is: ZLL =2Z1(Z2+ZLV)Z3 Z1Z3+ (Z2+ZLV)Z3+Z1(Z2+ZLV ). (31) L1 L=31.2 mH L2 L=31.2 mH L3 L=31.2 mH R1 R=10 Ohm R2 R=10 Ohm R3 R=10 Ohm L4 L=20.9 H L5 L=20.9 H L6 L=20.9 H R4 R=1 MOhm R5 R=1 MOhm R6 R=1 MOhm C3 C=250 pF C2 C=250 pF C4 C=250 pF R7 R=0.5 MOhm R8 R=0.5 MOhm R9 R=0.5 MOhm b c a n C A B G Z1 Z2Z3ZLV P ima y side (medium ol age) Seconda y side (low ol age) Figu e 3. A ans o me impedance model o simula e he powe line communica ion (PLC) communica ion in a medium- ol age line. A good ma ch be ween he designed model and he eal ans o me is illus a ed in Figu es 4and 5 , which compa e he measu ed and modeled impedances o a ans o me wi h a sho -ci cui on he low- ol age side. Impo an ly, he model exhibi s sa is ac o y ag eemen also wi h open-ci cui measu emen s on he low- ol age side. Fo he equency bands ha a e ele an o he PLC communica ion, he ypical impedance o he medium- ol age side o a ans o me anges om hund eds o Ω o ens o k Ω ; howe e , o equencies in close p oximi y o he esonan equencies, he impedance may ise up o housands o k Ω . I can be obse ed ha he impedance be ween a phase and he g ound is lowe han ha be ween he phases. The model aims o add ess equencies below 1 MHz, as such solu ion acili a es he modeling o i ually all na owband powe line communica ions. The measu emen s desc ibed in [ 27 ], and Re . [ 28 ] enable us o claim ha he model is sui able o simula ing mos MV/LV ans o me s, albei wi h he necessi y o adjus he esis ance, induc ance, and capaci ance by using he esonan equencies o he ele an ans o me . In indi idual ans o me s, Ene gies 2017,10, 816 9 o 16 he esonan equencies a e o en speci ied wi hin he da a shee , as such in o ma ion is used o Sweep F equency Response Analysis es s. Conside ing he measu emen s p esen ed in [ 29 , 30 ], he model can be u he cha ac e ized as applicable o high - ol age (HV)/MV ans o me s oo; ou own measu emen s and he esul s discussed wi hin [ 27 ] ne e heless also show ha he model is un o una ely no sui able o simula ing he LV side o an MV/LV ans o me . 30 40 50 60 70 80 90 100 0 50 100 150 200 [kHz] |Z| [kOhm] 30 40 50 60 70 80 90 100 −2 0 2 [kHz] phi(Z) [ ad] 100 200 300 400 500 600 700 800 900 1000 0 10 20 30 [kHz] |Z| [kOhm] 100 200 300 400 500 600 700 800 900 1000 −2 0 2 [kHz] phi(Z) [ ad] 10−1 100101102103 10−2 100 102 104 [kHz] |Z| [kOhm] 100102 −2 0 2 [kHz] phi(Z) [ ad] Model Measu emen Figu e 4. A compa ison o he measu ed and modeled impedances o he T0326/22 ans o me in—be ween he phases o he medium ol age side, wi h a sho ci cui a he low ol age side. 30 40 50 60 70 80 90 100 0 20 40 60 [kHz] |Z| [kOhm] 30 40 50 60 70 80 90 100 −2 0 2 [kHz] phi(Z) [ ad] 100 200 300 400 500 600 700 800 900 1000 0 2 4 6 8 10 [kHz] |Z| [kOhm] 100 200 300 400 500 600 700 800 900 1000 −2 0 2 [kHz] phi(Z) [ ad] 10−1 100101102103 10−5 100 105 [kHz] |Z| [kOhm] 100102 −2 0 2 [kHz] phi(Z) [ ad] Model Meau emen Figu e 5. A compa ison o he measu ed and modeled impedances o he T0326/22 in—be ween he phases and he g ound o he medium ol age side, wi h a sho ci cui a he low- ol age side. Ene gies 2017,10, 816 16 o 16 27. Kikke , C. A PLC equency model o 3 phase powe dis ibu ion ans o me s. In P oceedings o he 2012 IEEE Thi d In e na ional Con e ence on Sma G id Communica ions (Sma G idComm), Tainan, Taiwan, 5–8 No embe 2012; pp. 205–210. 28. S iphuek, R.; Cho igo, S. Low-cos equency esponse analyze o ans o me diagnosis. In P oceedings o he 2012 In e na ional Con e ence on Condi ion Moni o ing and Diagnosis (CMD), Bali, Indonesia, 23–27 Sep embe 2012; pp. 437–441. 29. Pham, D.; Pham, T.; Bo si, H.; Gockenbach, E. A new me hod o pu poses o ailu e diagnos ics and FRA in e p e a ion applicable o powe ans o me s. IEEE T ans. Dielec . Elec . Insul. 2013,20, 2026–2034. 30. B and , M.; Peniak, A. Iden i ica ion o he powe ans o me 110/23 kV ailu e. In P oceedings o he 2014 ELEKTRO, Rajecke Teplice, Slo akia, 19–20 May 2014; pp. 531–534. 31. Zimme mann, M.; Dos e , K. An analysis o he b oadband noise scena io in powe line ne wo ks. In P oceedings o he In e na ional Symposium on Powe line Communica ions and i s Applica ions (ISPLC2000), Lime ick, I eland, 5–7 Ap il 2000; pp. 5–7. 32. Zheng, T.; Yang, X.; Zhang, B.; Chen, J.; Y, Z.; Tian, T. Resea ch o Noise Cha ac e is ics o 10-kV Medium-Vol age Powe Lines. IEEE T ans. Powe Deli . 2007,22, 142–150. c 2017 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h p://c ea i ecommons.o g/licenses/by/4.0/).