Voltage enhancement in dye-sensitized solar cell using (001)-oriented anatase TiO2nanosheets
ORIGINAL PAPER
Voltage enhancement in dye-sensitized solar
cell using (001)-oriented anatase TiO 2nanosheets
Barbora Laskova &Marketa Zukalova &
Ladislav Kavan &Alison Chou &Paul Liska &
Zhang Wei &Liu Bin &Pavel Kubat &Elham Ghadiri &Jacques E.Moser &Michael Gr?tzel
Received:13November 2011/Revised:13March 2012/Accepted:15March 2012/Published online:11April 2012#The Author(s)2012.This article is published with open access at https://www.wendangku.net/doc/e717441073.html,
Abstract A nanocrystalline TiO 2(anatase)nanosheet ex-posing mainly the (001)crystal faces was tested as photo-anode material in dye-sensitized solar cells.The nanosheets were prepared by hydrothermal growth in HF medium.Good-quality thin films were deposited on F-doped SnO 2
support from the TiO 2suspension in ethanolic or aqueous media.The anatase (001)face adsorbs a smaller amount of the used dye sensitizer (C101)per unit area than the (101)face which was tested as a reference.The corresponding solar cell with sensitized (001)-nanosheet photoanode exhibits a larger open-circuit voltage than the reference cell with (101)-terminated anatase nanocrystals.The voltage enhancement is attributed to the negative shift of flatband potential for the (001)face.This conclusion rationalizes earlier works on similar systems,and it indicates that careful control of experimental conditions is needed to extract the effect of band energetic on the current/voltage character-istics of dye-sensitized solar cell.Keywords Titanium dioxide .Anatase .Dye-sensitized solar cell
Introduction
Dye-sensitized solar cell (DSC),also called Gr?tzel cell,represents an attractive alternative of solid state photovol-taics due to high efficiency,low cost,and easy fabrication [1–4].Optimization of TiO 2photoanode for dye-sensitized solar cell has been a subject of numerous studies,and nano-crystalline anatase turned out to be the best material for this device [5].The voltage enhancement is crucial for further improvement of DSCs [1,3,6–10].Promising data were acquired recently by replacing the traditional electrolyte redox relay,I 3?/I -by other systems [3,6–10],but little is known about the voltage enhancement via tuning of the photoanode material.
The (101)face is dominating in ordinary TiO 2(anatase)materials (>94%of the total surface area of crystals)[11].The remaining face on the anatase crystal is (001)which is
https://www.wendangku.net/doc/e717441073.html,skova :M.Zukalova :L.Kavan (*):P.Kubat J.HeyrovskyInstitute of Physical Chemistry,v.v.i.,Academy of Sciences of the Czech Republic,Dolej ?kova 3,
18223Prague 8,Czech Republic e-mail:kavan@jh-inst.cas.cz
https://www.wendangku.net/doc/e717441073.html,skova :L.Kavan
Department of Inorganic Chemistry,Faculty of Science,Charles University,Hlavova 2030,
12843Prague 2,Czech Republic
A.Chou
ARC Centre of Excellence for Functional Nanomaterials,The University of Queensland,Level 5,AIBN Building No.75,Corner College and Cooper Roads,St Lucia,Queensland 4072,Australia
P.Liska :M.Gr?tzel
Laboratory of Photonics and Interfaces,
Institute of Chemical Sciences and Engineering,Swiss Federal Institute of Technology,1015Lausanne,Switzerland
Z.Wei :L.Bin
Department of Chemical and Biomolecular Engineering,National University of Singapore,Singapore 117576,Singapore
E.Ghadiri :J.E.Moser
Photochemical Dynamics Group,Institute of Chemical Sciences and Engineering,Swiss Federal Institute of Technology,1015Lausanne,Switzerland
J Solid State Electrochem (2012)16:2993–3001DOI 10.1007/s10008-012-1729-0
consistent with the conclusion that a truncated bipyramid is the corresponding crystal morphology[12].Only rarely,the rhombic-shaped crystals are found,exposing the(010)face [13].Both(001)and(010)facets are called“high-energy”or“reactive”ones,and they show interesting activity in catalysis and photocatalysis[13–16].
Comparative studies of anatase(101)or(001)faces have been carried out on macroscopic single-crystal electrodes [17,18],but the dye sensitization was attempted only on the (101)face of the single-crystal electrode[17].The works on single-crystal electrodes confirmed that the(001)face had more negative flatband potential and was more active for Li insertion than the(101)face[18].The conclusion about flatband potential shift was later reproduced on polycrystal-line electrodes[19].Also,the improved Li insertion was subsequently confirmed on polycrystalline(001)-oriented nanosheets[20].They were prepared hydrothermally in HF medium according to Yang et al.[11],and the follow-up studies[14,15,21–23]report on materials enriched up to 90%with the(001)face.
Recently,Wang et al.[24]studied the sensitization of such(001)nanosheets by CdS quantum dots,but no com-parison with(101)-exposing crystals was presented.This was carried out earlier by Yu et al.[25],who observed improved conversion efficiency of a DSC employing hydro-thermally grown nanosheets sensitized by the organometal-lic dye,N719[chemical name:di-tetrabutylammonium cis-bis(isothiocyanato)bis(2,2′-bipyridyl-4,4′dicarboxylato)ru-thenium(II)],as the photoanode material.They attributed the improvement to three effects specific for the(001)-oriented nanosheets:(1)enhanced diffusion of the electrolyte,(2) more easy adsorption of the dye,and(3)fewer defects in the surface.However,there were no clear experimental data about electrolyte diffusion and defects,and the amount of adsorbed dye(N719)was actually smaller on nanosheets than that on nanoparticles[25]which seems to contradict the statement(2).Yang et al.[23]reported recently on hierar-chical spheres with over90%(001)faces which were more active than the Degussa P25titania material in dye-sensitized solar cells,and the effect was ascribed to(1) stronger ability to dissociatively“absorb”(COOH)groups, (2)higher surface area for dye loading,(3)light scattering, and(4)smaller electron losses at grain interfaces[23]. However,these conclusions were not supported by direct experimental data.Zhang et al.[26]tested the(001)-ex-posed microspheres in a bilayer photoanode with Degussa P25underlayer,and concluded that the beneficial effect consists in enhanced light scattering on the mirror-like (001)facets.
To address these divergences,we report here on a com-parative study showing that a significant effect favoring the (001)nanosheets is the enhanced open-circuit voltage of the solar cell.This result is consistent with the negative shift of flatband potential of the(001)face.To the best of our
knowledge,this conclusion is presented here for the first
time;hence,it upgrades earlier works dealing with these
problems[23,25,26].
Experimental section
Materials
Anatase TiO2nanosheets were prepared as follows:10mL
of titanium(IV)butoxide was mixed with0.8–1.2mL of
hydrofluoric acid(concentration,≈50%).The mixture was
sealed in a Teflon cell encased in a stainless steel autoclave
and heated at180–200°C for24h.A sample was then
collected,washed with copious amounts of Milli-Q water
and finally dried at100°C.The reference material was
prepared in the same way,but in the absence of HF which
was replaced by the same amount of water.X-ray diffraction
patterns(data not shown)confirmed that the reference ma-
terial was phase-pure anatase.For comparison,a second
reference material(coded C240)[27]was also used.It is
nanocrystalline anatase,S BET089m2/g,prepared by hydro-lysis of titanium tetra(iso propoxide)and hydrothermal re-
crystallization at240°C in the absence of HF[28].The
crystal morphology of C240is characterized by particles ca.
10–20nm in size exposing mainly the(101)facets,and it is
frequently used for DSC[29].The photoelectrochemical
behavior of both reference materials was very similar.
Electrodes from all parent powder materials(see above)
were fabricated using either aqueous paste(A films)or
simply ethanolic suspension(E films).The aqueous paste
was prepared as follows:0.3g of the powder was mixed
under slow addition of4×0.15mL of10%aqueous solu-
tion of acetylacetone,0.3mL of4%aqueous solution of
hydroxypropylcellulose(MW100,000),and0.3mL of
10%aqueous solution of Triton-X100.The obtained slurry
was deposited on F-doped SnO2(FTO)glass(TEC15from
Libbey-Owens-Ford,15Ω/sq)with Kapton foil tape defin-
ing the TiO2film edges.The film was then calcined for
30min in air at450°C.For the preparation of E film
electrodes,the powder samples were sonicated in ethanol.
The obtained slurry was deposited by doctor blading,and a
uniform semitransparent film was obtained after drying at
room temperature and calcination in air at450°C.Typical
film thickness was2–4μm(Alpha-step profilometer,Tencor
Instruments)for both A/E films.
The C101dye[NaRu(4,4′-bis(5-hexylthiophene-2-yl)-
2,2′-bipyridine)(4-carboxylic acid-4′-carboxylate-2,2′-
bipyridine)(NCS)2]with chenodeoxycholic acid(cheno)as
a coadsorbent was used for sensitization(see[30]for
details).Immediately after calcination,the still warm elec-
trode(ca.50°C)was dipped in a solution containing
300μmol/L of C101dye and300μmol/L cheno in a mixed
solvent of acetonitrile+t-butanol solution(1:1,v/v).The
electrodes were soaked at room temperature in the solution
overnight to secure complete attachment of the sensitizer
dye to the electrode surface.To avoid irregularities in dye
attachment[31],the sensitization time and temperature were
identical for all the tested electrodes.The DSC was assem-
bled with platinized F-doped tin oxide(FTO)counter elec-
trode[32,33]using a Surlyn tape(25μm in thickness)as a
seal and spacer.The electrolyte solution was0.6M N-
methyl-N-butyl imidazolium iodide,40mM I2,0.075M
lithium iodide,0.26M tert-butylpyridine,and0.05M guani-
dine thiocyanate in acetonitrile/valeronitrile(85/15%,v/v).
The cell active area for illumination was0.22cm2,defined by
a mask.
Methods
The X-ray diffraction(XRD)was investigated on powder
samples by XRD-6000,Shimadzu,Japan,using Ni-filtered
CuKαradiation(λ00.15418nm).The transmission electron
microscopy(TEM)images were measured on a JEOL JEM-
2010F microscope.The BET surface areas of the prepared
powder materials were determined from nitrogen adsorption
isotherms at77K using the Micromeritics ASAP2020
instrument.The surface areas of thin films were determined
from Kr-adsorption isotherms,which were measured directly
on the sintered films following the methodology described in
[34].The surface concentration of the C101dye on TiO2was
measured spectrophotometrically as follows:The sensitized
electrode was dipped in0.1M tetrabutylammonium hydrox-
ide in dimethylformamide and stirred until complete desorp-
tion into the liquid took place.The solution was analyzed on
the PerkinElmer Lambda1050spectrometer using the extinc-
tion coefficientε550017.5·103M?1cm?1[30].The dye surface coverage(Гdye)was determined by normalizing the found dye
concentration to the film's physical surface area from Kr-
adsorption isotherm.Scanning electron microscopy(SEM)
and energy-dispersive X-ray analysis(EDX)were carried
out with the Hitachi FE SEM S-4800microscope equipped
with the Noran EDX system.Electrochemical measurements
were carried out in a one-compartment cell using an Autolab
Pgstat-30(Ecochemie)controlled by GPES-4software.For
photoelectrochemical tests,the light source was a450-W
xenon light source(Osram XBO450,Germany)with a filter
(Schott113).The light power was regulated to the AM1.5G
solar standard by using a reference Si photodiode equipped
with a color-matched filter(KG-3,Schott)to reduce the mis-
match in the region of350–750nm between the simulated
light and AM1.5G to less than4%.The differing intensities
were regulated with a neutral wire mesh attenuator.The ap-
plied potential and cell current were measured using a Keithley model2400digital source meter.Optical determina-tion of the flatband potential was made by a spectroelectro-chemical method described in[35–37].The measurement was carried out in0.2M NaClO4(pH adjusted by HClO4or NaOH)using UV–vis–NIR spectrometer PerkinElmer Lambda1050interfaced to a potentiostat.Measurements were performed in transmission mode at gradually decreasing potentials from0V to?1.2or?1.4V.Potential was set,and after1.5min at the given potential,the spectrum was mea-sured.For data processing,the measured spectra were nor-malized by subtracting the spectrum measured at0V. Nanosecond flash photolysis was applied to C101dye-sensitized transparent TiO2layers covered by a film of pure methoxypropionitrile and a thin cover glass.Pulsed excitation (λ0530nm,5-ns FWHM pulse duration,20-Hz repetition rate)was provided by an optical parametric oscillator(GWU OPO-355),pumped by a frequency-tripled,Q-switched Nd: YAG laser(Continuum,Powerlite7030).The laser beam output was expanded by plano-concave lens to irradiate a large cross section of the sample,whose surface was kept at a30°angle to the excitation beam.The probe light,produced by a Xe arc lamp,passed through the first monochromator, various optics,and the sample.Transmitted light was focused on the entrance slit of the second monochromator and detected by a fast photomultiplier tube.Data waves were recorded on a DSA602A digital signal analyzer(Tektronix).Satisfactory signal-to-noise ratios were typically obtained by averaging over3,000laser shots.
Results and discussion
Figure1a shows a typical X-ray diffraction pattern of TiO2 nanosheets(grown in HF medium),indicating the formation of pure anatase TiO2(JCPDS no.21–1272).The diffracto-grams of(001)nanosheets are similar to those of(101)-nanoparticles,which is in accord with earlier literature[11, 14,15,21,22].As XRD is obviously not very sensitive to distinguish the(001)or(101)oriented anatase crystals,the morphology of our TiO2anatase nanosheets was character-ized by transmission electron microscopy.A typical nano-sheet dimension was40·30·7nm3(Fig.1b).Figure1c shows a high-magnification TEM image of two selected individual TiO2nanosheets(ca.30·20·7nm3in size).The lattice spac-ing parallel to the top and bottom facets was determined to be～0.235nm,corresponding to the(001)planes of anatase TiO2.Figure1d shows the corresponding selected-area elec-tron diffraction(SAED)pattern(indexed as the(001)zone axis diffraction).It further indicates that the top and bottom facets of the nanosheets are the(001)planes.The anatase nanosheets exhibited a specific surface area from nitrogen adsorption measurement,S BET between85and120m2/g depending on the sample batch.Higher values were
observed in products grown from mixtures containing less HF and autoclaved at lower temperatures (see “Experimental section ”).The typical nanosheet dimension of 40·30·7nm 3(cf.Fig.1b )translates into the calculated S BET of 103m 2/g,which matches reasonably well the experimental values from adsorption isotherms.The particles grown in HF-free medium had S BET 0150m 2/g and exhibited the usual bipyramidal crystal shape with (101)facets.This morphology resembles that of C240particles optimized earlier for DSC applications [29].
SEM images of our nanosheet-based electrodes are shown in Fig.2.Both variants of TiO 2film deposition (A films,E films;see “Experimental section ”)exhibited a sim-ilar morphology of unorganized nanoplatelets which were reasonably uniform and non-agglomerated.This is benefi-cial for achieving good optical and mechanical quality of the films.It should be noted that even the E films were optically semitransparent with good adhesion to the FTO support in spite of the very simple deposition procedure used and the fact that particles were not stabilized against agglomeration by any other additives as in the case of A films (see “Experimental section ”).The as-received nanosheet material
contained 8wt%of F,as determined by EDX analysis,but the heat treatment during electrode fabrication (450°C,30min;see “Experimental section )caused the F content to drop practically to zero for both the A and E films.
The actual surface area of electrodes (determined from the Kr-adsorption isotherm of the thin-film samples)was normalized to the projected geometric area,which provided the roughness factor.The found values of roughness factor were from 100to 600for various film thicknesses,but without significant distinction between the A and E films.More importantly,the surface concentration of the dye (Гdye )was,for both film types (A,E),significantly smaller on the (001)films compared to that on (101)films (Table 1).The found Гdye for (101)films is comparable to the values reported earlier for various Ru-bipyridine sensitizers adsorbed on titania (from 0.56to 1.16molecules/nm 2;see [38]for the data overview).Recently,Sauvage et al.[31]studied the C101dye adsorption on a TiO 2film which was,obviously,rich in the (101)-terminated anatase particles.They found an almost perfect dye monolayer (assuming Гdye 00.57molecules/nm 2)only for the films sensitized at low temperature (4°C),but the dye coverage exceeded
the
Fig.1Structural
characteristics of (001)nanosheets.a XRD pattern.b Low-magnification TEM image.c High-magnification TEM image.d Typical
SAED pattern of an individual TiO 2nanosheet
monolayer saturation limit for the films sensitized at room or higher temperatures.In accord with this report,both our (101)films adsorb more C101dye than expected for a monolayer (Table 1).However,our Гdye values for the (001)films are below this limit.The relatively smaller dye loading on the (001)face was also reported for the N719dye [25],but the reason for smaller adsorption capacity of this face is unclear.The anchoring of N719and N3dyes [N3is cis -bis (isothiocyanato)bis (2,2′-bipyridyl-4,4′-dicarboxylato ruthenium(II)]on the (101)face was investigated carefully,including quantum chemical simulations [38,39],but there is no corresponding study of the (001)face nor that of other dyes like C101.
The trend that smaller values of Гdye are observed for the (001)films qualitatively agrees with the conclusion of Yu at al.[25]who reported that the surface concentration of N719dye was 143nmol/cm 2for the (001)nanosheets or 214nmol/cm 2for the reference (101)nanoparticles,respec-tively.However,the values reported by Yu et al.[25]do not seem to be normalized to the physical (BET)area of the TiO 2film as in our case.(Note that the recalculated Гdye for the physical surface area would be unrealistically high in the cited work [25],ca.a thousand molecules per square nano-meter).Also,we should note that our data in Table 1do not support the assumption of Yang et al.[23]that the (001)face has better ability to adsorb the N719dye.
Figure 3shows the current –voltage characteristics of a solar cell employing the dye-sensitized A films (Fig.3a )and E films (Fig.3b ).In both cases,data are plotted for (001)-oriented nanosheets (full curves)and reference (101)par-ticles (dashed curves).For the reference (101)particles,we report on the materials grown from Ti(IV)butoxide in HF-free medium (S BET 0150m 2/g),but the plots for our second (101)reference (C240,S BET 089m 2/g)were quite similar (data not shown).Detailed results about our solar cells are collected in Table 1.It is obvious that the (001)-oriented nanosheet films exhibit smaller short-circuit photocurrents (I sc ),particularly at 100%sun illumination,when the light harvesting is less efficient,and also,the Гdye concentrations are lower (Table 1).Hence,we attribute the smaller I sc to smaller dye loading on the (001)nanosheets.At 10%sun,the differences in photocurrents are less pronounced or even negligible (A film,Fig.3a ).The (101)particles in A film further show superlinear response to light intensity which might be caused by some dye aggregation.This effect,albeit less pronounced,is also expressed for the remaining films in Table 1.It is further illustrated by higher ηvalues for higher light https://www.wendangku.net/doc/e717441073.html,ually,we observe opposite trends [30],but there are also examples when ηand light intensity do not scale monotonically for dyes of this type [40].Furthermore,there is no proportionality between the efficiency,η,and Гdye (Table 1).This finding is supported by Sauvage et al.[31]who reported on decreasing efficiency for the C101-sensitized films,if the Гdye was larger than the mono-layer coverage.They concluded that subtle structural characteristics at the C101/TiO 2interface influence
the
Fig.2Scanning electron microscopy images of the FTO-deposited film from (001)-oriented nanosheets.Left :A film,right :E film
Table 1Characteristics of dye-sensitized solar cells with various TiO 2films Film type
Гdye [molecules/nm 2]
10%sun 100%sun I sc [mA/cm 2]
U oc [mV]FF η[%]I sc [mA/cm 2]U oc [mV]FF η[%]A-(001)0.40.866200.74 4.28.787080.69 4.3A-(101)0.70.895660.73 3.810.46600.69 4.7E-(001)0.50.516250.74 2.5 5.347250.72 2.8E-(101)
0.8
0.65
583
0.72
2.8
6.36
681
0.71
3.1
Гdye surface concentration of the C101dye in molecules per square nanometer,I sc short-circuit photocurrent,U oc open-circuit voltage,FF fill factor,ηsolar conversion efficiency
electron transfer dynamics and light harvesting of the assembly [31].
The actually measured photocurrent is further dependent on the TiO 2film thickness.This is difficult to control accurately in various film-deposition techniques;hence,the matching of photocurrents in Fig.3a (10%sun)is casual only.From this point of view,we should consider with care the conclusion by Yu at al.[25]who observed a larger photocurrent for the (001)nanosheets,compared to that for (101)nanoparticles and reference commercial titania (P25,Degussa).They reported a film thickness of “about 10μm,”but the surface concentration of the used dye (N719)was actually smaller by a factor of ca.1.5on the (001)nanosheets compared to that on their reference (101)nanoparticles [25].The relatively smaller dye loading for (001)nanosheets compared to that on (101)particles was also reproduced by us (see Гdye values in Table 1).At full sun illumination,our solar conversion efficiencies ηare slightly better for the (101)-terminated nanocrystals.This is due to the dominating contribution of enhanced photocur-rent for this face.Our conclusion is in conflict with Yu et al.[25]who reported just the opposite trend in photocurrents and ηvalues.
Figure 3and Table 1demonstrate that the most pro-nounced effect distinguishing (001)nanosheets from the ordinary (101)nanoparticles is the open-circuit voltage (U oc )enhancement of the former.The found differences in open-circuit voltage between nanosheets and nanoparticles (ΔU oc )were 54or 48mV (for A films at 10or 100%sun,respectively)and 42or 44mV for E films at the corresponding conditions and for the actual experiments demonstrated in Table 1.It should be noted that these numbers (and the data in Fig.3and Table 1)represent only a single set of measure-ments;hence,experimental errors and the likely sample-to-sample variations could be unnoticed.To avoid such mistakes,we have carried out a statistical evaluation of data using an array of parallel tests on various TiO 2films with a different preparation history.This analysis showed statistically
insignificant differences between A and E films.The averaged values for both film types (A,E)were as follows:ΔU oc ?47?3eTmV at 10%sun illumination ΔU oc ?45?2eTmV at 100%sun illumination
Obviously,even the dependence on the light intensity is not very pronounced too.This points at the hypothesis,that ΔU oc reflects a fundamental physical effect (albeit small)but not a variable introduced by experimental conditions,such as film thickness,preparation history,dye loading,light intensity,etc.More specifically,one of the reasons for positive values of ΔU oc can be the corresponding shift of flatband potential of (001)faces/(101)faces.
Similarly enhanced voltage (ΔU oc 020mV)was found for 001-terminated anatase in hierarchical spheres,referred to the value for P25particles [23].However,the enhance-ment was not discussed in [23]and we should also note that P25is hardly the optimum reference material.It is,actually,a mixture of anatase and rutile,while both phases exhibit a significantly different electronic structure:e.g.,the flatband potential of rutile is by 0.2V more positive than the value for anatase [17].
In contrast to these data,Yu et al.[25]reported on negligible differences in U oc for their (001)nanosheets,(101)nanoparticles,and the P25film sensitized by N719.To address this paradox,we should note that Yu et al.[25]found a considerably smaller U oc (ca.580to 590mV at 100%sun)for their DSCs compared to our values (Table 1).Smaller U oc values may stem from a voltage drop caused by enhanced recombination of photoinjected electrons in the titania conduction band with the electrolyte [4,41],and this effect can mask any other mechanism of fine tuning of U oc ,e.g.,by crystal face orientation.
Our combination of cheno-coadsorbent with high-extinction dye (C101)provides,obviously,a more-defined interface for exploring small U oc shifts undisturbed by such parasitic effects.Cheno improves the dye attachment by assembling the geometry of the surface complex,prevents
C u r r e n t d e n s i t y (m A /c m 2)
C u r r e n t d e n s i t y (m A /c m 2)
Cell voltage (V)Cell voltage (V)
a
b
Fig.3Current –voltage
characteristics of dye-sensitized solar cells employing
C101-sensitized TiO 2photoa-node either from (001)-oriented nanosheets (solid red lines )or reference (101)nanoparticles (dashed blue lines ).a A films,b E films
agglomeration of dye molecules,and decreases the recom-bination losses with the electrolyte solution [30,42,43].Furthermore,the back electron transfer can be hindered by a compact titania underlayer on top of the FTO support [4].This strategy is unsuitable for our study,aiming at the distinction of (001)-and (101)-terminated nanocrystals,but we should note that the optimization of the morphology of TiO 2photoanode may further enhance U oc for a DSC device quite similar to ours [30].Hence,the elimination of all the other factors influencing ΔU oc is essential,if subtle effects caused by band energetic are to be unraveled.
To test our hypothesis about different band energetic,Fig.4compares spectroelectrochemical data for thin-film electrodes made from (001)-and (101)-terminated nano-crystals.This technique was developed for determination of the flatband potential of transparent semiconductors,and it is particularly useful for nanocrystalline electrodes where the standard method based on electrochemical imped-ance (Mott –Schottky plots)is complicated by various factors [35–37].The flatband potential of anatase,E fb (in volts)is known to exhibit Nernstian dependence on pH:E fb ?E 0à0:0591pH
e1T
where the constant E 0was reported to be ?0.4V for the (101)face assuming a saturated calomel electrode (SCE)as the reference electrode [17,35,36].The negative shift of absor-bance/potential profiles for the (001)-oriented film is apparent from Fig.4,although the absorbance onset potential is not that clearly different.This might be due to surface states which contribute differently in (001)or (101)films.Based on optical spectra and X-ray photoelectron spectroscopy (XPS),Pan et al.[16]concluded that the conduction band edge of (001)face is upshifted (in electrochemical scale)by 0.04V.This
contradicts our conclusion,as well as earlier spectroelectro-chemical reports on single-crystal [18]and polycrystalline [19]electrodes.(One of the reasons for this discrepancy might be that the reported upshift is within experimental error of the determination of the valence band edge by XPS [16].)
Our data are in qualitative accord with the earlier conclu-sion by Kawakita et al.[19]based on Mott –Schottky plots for (001)-vs .(101)-oriented nanocrystals similar to ours.These authors reported on negative shift of E fb for their (001)-oriented nanocrystals;the E fb values were from ca.?0.4to 0V vs.SCE for various samples at pH 6(phosphate buffer).This is more positive than the value of E fb ≈?0.75V predicted by Eq.(1),but the difference was not commented on in [19].As discussed above,accurate imped-ance data are available for single-crystal electrodes only;in this case,the E fb values for (001)face were negatively shifted by 0.06V compared to that of (101)face [18].This negative shift of E fb is not far from the observed enhancement of open-circuit voltage,ΔU oc of ca.0.04V found in this study (vide ultra).However,there might be also other effects at play,such as different geometry of the dye/titania surface complex [44].To get further insight into the specific behavior of (001)nanosheets referenced to that of (101)nanoparticles,we employed transient absorption spectroscopy.Nanosecond flash excitation was applied to C101-sensitized TiO 2film contacting pure methoxypropionitrile solvent.Monitoring the transient absorbance signal at a wavelength λ0650nm allowed to follow the time course of the dye cation S +produced upon ultrafast electron injection from the photo-excited sensitizer,S*,into the conduction band of TiO 2(Eq.2).In the absence of electrolyte (redox mediator),the
A b s o r b a n c e
Potential (V vs. SCE)
Fig.4Optical absorbance of TiO 2films from (001)-or (101)-oriented nanosheets plotted by open red points or full blue points ,respectively.The absorbance was measured at 640nm and normalized to the mass of the TiO 2film.It is plotted as a function of the applied electrochem-ical potential in 0.2M NaClO 4at two different pH values.The lines are guides to the eye
43210-1
A b s o r b a n c e c h a n g e * 104
800
600
400
200
Time (μs)
(001)-nanosheets
(101)-nanoparticles
Fig.5Temporal behavior of the transient absorbance measured at λ0650nm for a C101dye-sensitized anatase (001)-nanosheet film,cov-ered by pure methoxypropionitrile solvent,upon ns-pulsed laser exci-tation (red trace ).A typical transient absorbance decay curve obtained in identical conditions with (101)nanoparticles is shown for compar-ison (blue trace ).Amplitudes of both signals were normalized at time zero for a better visual comparison.The first-order kinetic fits are indicated on top of each experimental curve
decay of the S +signal was due to the back electron transfer reaction (Eq.3).
S TiO 2th n !S ?j j TiO 2!S tte àcb TiO 2eTe2TS tte àcb TiO 2eT!S j TiO 2
e3T
The excitation pulse fluence was progressively decreased by neutral density filters until the signal displayed a single exponential decay (Fig.5).The used fluence of 35μJ/cm 2was then believed to relate to the injection of at most one electron per TiO 2nanoparticle or nanosheet.The transport of charges between individual nanoparticles or nanosheets is negligible within the sub-millisecond time frame of the back electron transfer process.
The corresponding rate constant,k b (Eq.3),can be obtained from first-order kinetic fit of the absorbance change,ΔA :
ΔA ?C tB áexp àk b át eT
e4T
where t is time and C and B are constants.The fitted values of k b are: 1.2·103s ?1for the (001)nanosheets and 7.7·103s ?1for the (101)nanoparticles,respectively.Hence,the back electron transfer is by a factor of 6slower for the (001)nanosheets compared to the same process on (101)nanoparticles.The difference in the back electron transfer kinetics observed for both samples could be rationalized by a change in the dye-anchoring geometry.Assuming a damp-ing coefficient β01.2?–1for through-space electron tun-neling (Eq.5),retardation of the charge recombination reaction by a factor of 6corresponds to the increase of the electron transfer distance existing between the Ru(III)center of the oxidized dye and the closest Ti(IV)site on the surface of the oxide by Δr 01.5?:k b ?k 0b áexp àb Δr eT
e5T
C101has only two carboxylic anchoring groups available on a single bpy ligand.The distance between the Ru ion and the TiO 2thus depends strongly upon the tilt angle of the pyridyl rings on the surface.Because the dicarboxylated bpy ligand (bi-isonicotinic acid)tends to distort upon anchoring on the TiO 2surface,different geometries are expected on the (101)and (001)surfaces [45].The distance between the Ru center of the dye and the Ti 4+ion directly linked to one of the oxygen atoms of the carboxylic anchor is ≈10?when the bpy adopts a flat structure.A change of the tilt angle of the pyridyl rings related to the surface normal of ca.15°on the (001)facet to ca.35°on the (101)facet would yield a decrease of the distance between the Ru center in the dye to the surface:Δr ?10ácos15à10ácos35%1:5?
e6T
which is the Δr value calculated from our experimental data (Eq.5).
In DSCs,the back electron transfer process competes kinetically with the regeneration of the dye by the donor species of the electrolyte.As the latter reaction should not depend upon the crystalline face on which the dye is adsorbed,the retardation of the back electron transfer can only improve the charge separation yield.The difference in back electron transfer rate (k b )hardly influences the open-circuit voltage of the cell.The U OC certainly depends on the injected electrons'quasi-Fermi level [2,4].However,the electrons'lifetime is controlled by the competition between their transport in the TiO 2network and their recombination with the oxidized mediator (I 3–).The recombination be-tween conduction-band electrons and the dye cations,S +,is generally sufficiently intercepted by the reduction of S +by I ?and is not expected to influence the potential of DSC.
Conclusion
Nanocrystalline TiO 2(anatase)in two different crystal mor-phologies exposing mainly the (001)or (101)crystal faces was employed as a photoanode material in dye-sensitized solar cells.The (001)face adsorbs a smaller amount of the used dye sensitizer (C101)but provides a larger open-circuit voltage of the solar cell.The negative shift of flatband potential is suggested to be responsible for the observed enhancement of U oc .This conclusion helps to rationalize contradictory data in the earlier literature.Furthermore,it indicates that careful control of experimental conditions is needed to extract the effect of band energetic on the current/voltage characteristics of the dye-sensitized solar cell.
Acknowledgments This work was supported by the Academy of Sciences of the Czech Republic (contracts IAA 400400804and KAN 200100801),Grant Agency of the Czech Republic (contract no.P108/12/0814),and the EC 7th FP project SANS (contract no.NMP-246124).B.L.thanks the National Research Foundation of Singapore (R279-000-276-272)for financial support.M.G.is very grateful to the European Research Council (ERC)for supporting his research under the ERC-2009-AdG grant no 247404MESOLIGHT.
Open Access This article is distributed under the terms of the Crea-tive Commons Attribution License which permits any use,distribution,and reproduction in any medium,provided the original author(s)and the source are credited.
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电压暂降科普之三：严重程度
电压暂降科普（3）——严重程度 本文系电压暂降系列文章第三篇接第二篇电压暂降科普（2）——根本原因之后 不同原因引起的电压暂降的特征和严重程度不同。如：三相铁芯饱和程度不同，变压器激磁引起的三相电压暂降的深度不同，变压器投切引起的电压暂降幅值（剩余电压）一般不低于80%，且含有谐波分量。短路引起的电压暂降的有效值波形通常为矩形，不同故障类型、故障位置引起的电压暂降的幅值和持续时间不同，变化范围较大。感应电机启动引起的电压暂降的电压有效值波形一般非矩形，电压下降较小，但持续时间较长。 暂降幅值和持续时间是刻画电压暂降事件的基本特征。单一的一次暂降事件，可用电压幅值-持续时间平面上的一个点表示。电压幅值的大小和持续时间的长短，可直观地反映电压暂降的严重程度。不同原因引起的电压暂降的严重程度在电压幅值-持续时间平面上的分布，如图6。 图6不同原因引起电压暂降的典型幅值-持续时间特性 可见，不同原因引起的电压暂降严重程度，在电压幅值-持续时间平面上的分布不同。输电网故障引起的电压暂降，深度较深（剩余电压较小），持续时间较短，约100ms；本地配电网故障引起的电压暂降，深度深（剩余电压小），持续时间长于输电网故障引起的电压暂降；远方配电网故障引起的电压暂降，深度较浅（剩余电压较大），持续时间与本地配电网故障引起的电压暂降较一致；大型电动机启动等引起的电压暂降，深度浅（剩余电压大），持续时间较长。 为了提高供电可靠性，本地配电网可能采用自动重合闸、熔断器和电流保护装置相互配合的方式清除故障。当本地配电网内发生故障时，首先由过流速断保护清除故障，在清除故障的断路器动作前会产生一个持续时间很短的电压暂降，持续时间几乎等于断路器动作时间；第一次故障清除后，发生电压中断，自动重合闸装置按整定的时间重合闸，如果重合闸成功，供电恢复，如果重合于故障，在配电馈线分支线上配置了熔断器保护的配电网中，需在熔断器清除故障的动作时间定值之后，由保护再次清除故障。通过保护时间定值与熔断器动作时间的配合，如果熔断器清除了故障，电流保护不再动作，供电可靠性得到了保证；如
电压降计算方法80181
电缆电压降 对于动力装置，例如发电机、变压器等配置的电力电缆，当传输距离较远时，例如900m，就应考虑电缆电压的“压降”问题，否则电缆采购、安装以后，方才发觉因未考虑压降，导致设备无法正常启动，而因此造成工程损失。 一.电力线路为何会产生“电压降”？ 电力线路的电压降是因为导体存在电阻。正因为此，所以不管导体采用哪种材料（铜，铝）都会造成线路一定的电压损耗，而这种损耗（压降）不大于本身电压的10%时一般是不会对线路的电力驱动产生后果的。 二.在哪些场合需要考虑电压降? 一般来说，线路长度不很长的场合，由于电压降非常有限，往往可以忽略“压降”的问题，例如线路只有几十米。但是，在一些较长的电力线路上如果忽略了电缆压降，电缆敷设后在启动设备可能会因电压太低，根本启动不了设备；或设备虽能启动，但处于低电压运行状态，时间长了损坏设备。 较长电力线路需要考虑压降的问题。所谓“长线路”一般是指电缆线路大于500米。 对电压精度要求较高的场合也要考虑压降。 三.如何计算电力线路的压降？ 一般来说，计算线路的压降并不复杂，可按以下步骤： 1.计算线路电流I 公式：I= P/1.732×U×cosθ 其中： P—功率，用“千瓦”U—电压，单位kV cosθ—功率因素，用0.8～0.85 2 .计算线路电阻R 公式：R=ρ×L/S 其中：ρ—导体电阻率，铜芯电缆用0.01740代入，铝导体用0.0283代入
L—线路长度，用“米”代入 S—电缆的标称截面 3.计算线路压降 公式：ΔU=I×R 举例说明： 某电力线路长度为600m，电机功率90kW，工作电压380v，电缆是70mm2铜芯电缆，试求电压降。 解：先求线路电流I I=P/1.732×U×cosθ=90÷（1.732×0.380×0.85）=161(A) 再求线路电阻R R=ρ×L/S=0.01740×600÷70=0.149(Ω) 现在可以求线路压降了： ΔU=I×R =161×0.149=23.99（V） 由于ΔU=23.99V，已经超出电压380V的5%（23.99÷380=6.3%），因此无法满足电压的要求。 解决方案：增大电缆截面或缩短线路长度。读者可以自行计算验正。 例：在800米外有30KW负荷，用70㎜2电缆看是否符合要求？ I=P/1.732*U*COS?=30/1.732*0.38*0.8=56.98A R=ρL/S=0.018*800/70=0.206欧 △U=IR=56.98*0.206=11.72<19V (5%U=0.05*380=19) 符合要求。 电压降的估算 1．用途
电压暂降科普之四：电压暂降特征
电压暂降科普之四：电压暂降特征 从物理现象看，电压暂降是母线电压方均根值下降至额定电压的90%~10%，持续0.5 周波~1min的扰动事件。相对于谐波、三相不平衡、电压波动与闪变等平稳电能质量扰动，电压暂降、短时电压中断、电压暂升等为非平稳扰动。前者需外部人为干预后才能消失，后者会自动消失。因此，前者被称作扰动现象或连续型扰动，后者被称作扰动事件或事件型扰动。区分两者的关键在于是否需要人工干预才能消失，这样，便于工程技术人员理解。 为了理解和分析电压暂降事件，用恰当的电压暂降特征刻画暂降事件是基础。 1、刻画形式 电压暂降事件的本质特性是电特性，表现为电压突然降低然后自动恢复的电压事件，表现为事件过程中电压随时间在持续较短时间内发生突然降低，然后突然恢复两次变化，可用三相电压瞬时值、有效值随时间变化的波形图、相量图、三相电压表达式等形式刻画。 以三相对称电压暂降为例，表现形式如图1、图2。 图1三相对称电压暂降瞬时值波形图和有效值波形图
图2三相对称电压暂降相量图 三相对称电压暂降的数学表达式如下，其中，V为发生电压暂降相的电压幅值。 其中，电压暂降事件的瞬时值波形图和有效值波形图，均能直观地刻画电压暂降事件中电压随时间的变化，而相量图和数学表达式是对电压暂降事件中某瞬间电压的描述。 2、暂降特征 暂降特征是人们对暂降事件的客观理解和认识，是由人定义的用于描述和刻画电压暂降事件的物理量。根据刻画目的、认知程度的不同，刻画电压暂降事件时采用的特征也不同。 根据需要和认知程度，用于刻画电压暂降事件的特征有多个，通常可用合理的特征向量刻画。刻画电压暂降的特征向量中的特征主要有：暂降幅值（剩余电压）、暂降持续时间、暂降频次等。其中，暂降频次是对某母线或系统暂降次数的统计，是对单一暂降事件的统计量，很多文献和著作中未当作电压暂降特征，但从全面刻画电压暂降事件的角度，尤其是需要分单一事件、节点和系统等不同层面进行电压暂降及其严重程度的刻画时，将暂降频次作为特征之一，具有一定的合理性。 在2014年IEEE颁布的标准IEEEStd1564中，定义了单一电压暂降事件指标、节点指标和系统指标等，这些均是用于刻画、描述和分析电压暂降事件及其严重程度的特征。 2.1暂降幅值 暂降幅值通常用剩余电压的方均根值表示，定义为电压暂降事件中，三相电压方均根值中电压最低一相的电压值。根据时域采样进行计算：
10KV电缆的线路损耗及电阻计算公式
10KV电缆的线路损耗及电阻计算公式 线损理论计算是降损节能，加强线损管理的一项重要的技术管理手段。通过理论计算可发现电能损失在电网中分布规律，通过计算分析能够暴露出管理和技术上的问题，对降损工作提供理论和技术依据，能够使降损工作抓住重点，提高节能降损的效益，使线损管理更加科学。所以在电网的建设改造过程以及正常管理中要经常进行线损理论计算。 线损理论计算是项繁琐复杂的工作，特别是配电线路和低压线路由于分支线多、负荷量大、数据多、情况复杂，这项工作难度更大。线损理论计算的方法很多，各有特点，精度也不同。这里介绍计算比较简单、精度比较高的方法。 理论线损计算的概念 1．输电线路损耗 当负荷电流通过线路时，在线路电阻上会产生功率损耗。 (1)单一线路有功功率损失计算公式为 △P＝I2R 式中△P--损失功率，W； I--负荷电流，A； R--导线电阻，Ω (2)三相电力线路 线路有功损失为 △P＝△PA十△PB十△PC＝3I2R (3)温度对导线电阻的影响： 导线电阻R不是恒定的，在电源频率一定的情况下，其阻值 随导线温度的变化而变化。 铜铝导线电阻温度系数为a＝0.004。 在有关的技术手册中给出的是20℃时的导线单位长度电阻值。但实际运行的电力线路周围的环境温度是变化的；另外；负载电流通过导线电阻时发热又使导线温度升高，所以导线中的实际电阻值，随环境、温度和负荷电流的变化而变化。为了减化计算，通常把导线电阴分为三个分量考虑：1）基本电阻20℃时的导线电阻值R20为 R20=RL 式中R--电线电阻率，Ω/km，; L--导线长度，km。 2）温度附加电阻Rt为 Rt=a（tP－20）R20 式中a--导线温度系数，铜、铝导线a=0．004； tP--平均环境温度，℃。 3）负载电流附加电阻Rl为 Rl= R20 4）线路实际电阻为 R=R20+Rt+Rl （4）线路电压降△U为 △U=U1－U2=LZ 2．配电变压器损耗(简称变损)功率△PB 配电变压器分为铁损(空载损耗)和铜损(负载损耗)两部分。铁损对某一型号变压器来说是固定的，与负载电流无关。铜损与变压器负载率的平方成正比。 配电网电能损失理论计算方法 配电网的电能损失，包括配电线路和配电变压器损失。由于配电网点多面广，结构复杂，客户用电性质不
如何计算电缆压降
如何计算电缆压降 问题1：电缆降压怎么算 50kw 300米采用vv电缆??? 25铜芯去线阻为 R=0.0172（300/25）=0.2 其压降为U=0.2*100=20 也就是说单线压降为20V 2相为40V 变压器低压端电压为400V 400-40=360V 铝线R=0.0283（300/35）=0.25 其压降为U=0.25*100=25 末端为350V 长时间运行对电机有影响建议使用 35铜芯或者50铝线 25铜芯其压降为 U=0.0172（300/35）=0.147（≈15V）15*2=30 末端为370V 铝线 U=0.0283（300/50）=0.17 17*2=34 末端为366V 可以正常使用（变压器电压段电压为400V) 50KW负荷额定电流I=P/1.732UcosΦ=50/1.732/0.38/0.8=50/0.53=94A 按安全载流量可以采用25平方毫米的铜电缆，算电压损失： R＝ρ(L/S)=0.017X300/25=0.2欧 电压损失U=IR=94X0.2=18V 如果用35平方毫米的铜电缆，算电压损失： R＝ρ(L/S)=0.017X300/35=0.15欧 电压损失U=IR=94X1.15=14V 选择导线的原则： 1)近距离按发热条件限制导线截面（安全载流量）； 2)远距离在安全载流量的基础上，按电压损失条件选择导线截面，要保证 负荷点的工作电压在合格范围； 3)大负荷按经济电流密度选择。 为了保证导线长时间连续运行所允许的电流密度称安全载流量。 一般规定是：铜线选5～8A／mm2；铝线选3～5A／mm2。 安全载流量还要根据导线的芯线使用环境的极限温度、冷却条件、敷设条件 等综合因素决定。 一般情况下，距离短、截面积小、散热好、气温低等，导线的导电能力强些， 安全载流选上限； 距离长、截面积大、散热不好、气温高、自然环境差等，导线的导电能力弱 些，安全载流选下限； 如导电能力，裸导线强于绝缘线，架空线强于电缆，埋于地下的电缆强于敷 设在地面的电缆等等。 问题2：55变压器，低压柜在距离变压器230米处。问变压器到低压柜需多粗电 缆 55KVA变压器额定输出电流(端电压400V)：I＝P/1.732/U＝55/1.732/0.4≈80(A) 距离：L＝230米，230米处允许电压为380V时，线与线电压降为20V，单根导线电压降：U＝10V，铜芯电线阻率：ρ＝0.0172 求单根线阻：R＝U/I＝10/80＝0.125(Ω) 求单根导线截面：S＝ρ×L/R＝0.0172×230/0.125≈32(平方) 取35 平方铜芯电线。 55KVA的变压器，最大工作电流约80A，输出电压400V。
电压暂降科普之九：损失评估
电压暂降科普（9）：损失评估 电能质量，尤其是电压暂降和短时中断给用户造成的损失不容忽视。2001年，美国支持数字化社会电力基础设施协会、美国电科院，对不同行业和地区985家企业的调查显示，美国每年电能质量损失约150-240亿美元;2007年，欧洲莱昂纳多电能质量工作协会估算，欧盟25国每年电能质量损失约1517亿欧元;我国2011年对上海100多家用户的调查显示，年经济性损失高达数十亿。电压暂降和短时中断，因其频次高，难预知，有较强的不确定性，采用不同定制电力技术均存在成本高且效果差异大的难题，因此，科学评估损失是采取低成本、高效益措施的前提。美国电科院统计的电能质量损失关系，如图1。其中，电压暂降损失占了几乎一半。 图1 电能质量给用户造成影响原因调查(美国) 统计表明，暂降损失在电能质量损失中占的比重最大，但实际中对此的认识广度和深度还很不足，在损失评估方法、损失构成和调查统计方法等方面，均值得完善，并使之更加理性。 1暂降损失评估方法暂降损失评估对于用户正确了解和认识电压暂降危害，采取合理措施具有重要意义。常用评估指标有：单次事件损失、单位产值损失(年暂降总损失与年产值之比)、单位功率损失(年暂降总损失与用户峰值功率之比)或单位用电量损失(年暂降总损失与年用电量之比)、暂降年损失等，用于比较单个暂降事件对不同行业、不同用户造成的损失，以及总损失。 《IEEE1346-1998评估供电和电子处理设备兼容性的推荐实施规程》提出了暂降损失直接评估法，流程如图2。
图2暂降损失直接评估法 直接法原理简单，易理解，但通过比较暂降严重程度与设备敏感度所确定的全年暂降引起的中断次数M与单次中断损失C，理论上可行，实际操作性不强。事实上，不同严重程度的暂降给用户造成的损失具有时空差异性。幅值低、持续时间长的暂降，可能类似电压中断造成的单次损失C;但幅值较高、持续时间较短的暂降，虽未导致经济活动中断，仅导致不正常，同样会造成损失，这样的损失评估难度更大。为此，有学者提出了影响因子或暂降风险评估法，结合中断损失评估用户暂降损失。 直接法的关键是单次暂降损失的确定。暂降损失的构成及其量化方法，一直存在争论，相关利益方，如：用户、供电企业、第三方参与者等，各自的出发点不同，对暂降损失的构成，认知差异大，对损失构成中损失值的确定也存在分歧。我国电压电流等级和频率标准化技术委员制定的《电能质量经济性评估第一部分：电力用户的经济性评估方法》中给出了电能质量经济损失的构成和各项损失的意义，具体见后文。实际上，暂降损失与用户经济活动有关，同类型同行业的不同用户之间存在较大差异，额定损失值难以推广;同时，用户经济活动具有时变性，损失大小也随之变化，确定额定值在不同情境下的可信度是尚需认识的问题。 直接法中不同暂降导致的损失不同，单次暂降损失量化困难。为此，有学者提出了间接法：可接受意愿法(WTA)和支付意愿法(WTP)。WTP是指用户愿意用一定数量的可支配货币采取措施提高电能质量的意愿，以此衡量用户对电能质量的评价。通常，给定一些场景，要求用户给出愿意支付的金额，以此作为暂降损失。WTA是指在给定场景下，用户对愿意接受的补偿的估计。WTA和WTP类似，均在假象场景下，由用户给出相应值，是用户对损失的主观角评价，对于用户的主观评价所涉及的诸多问题，以及其中蕴含的固有规律的认识，是完善间接法的必然要求。2暂降损失的构成近年来，通过媒体或其他途径，常听到暂降造成巨大损失的传闻，如：我国中部某厂宣称一次暂降损失13亿元;2010年，日本四日市东芝晶圆厂，一次70ms电压暂降造成2个月产量降低20%，损失上亿，导致全球闪存价格上涨10%。这些报道或传闻，无论损失数据的可信度如何，至少说明暂降损失不容忽视，且对暂降损失的理性认识急需加快。实际上的暂降损失或许没有报道或宣称值那么严重。因此，如何获得真实暂降损失很关键。为此，国内外学者和有关机构对暂降损失的构成进行了大量分析和调研，我国《电能质量经济性评估》标准给出了经济损失构成。该标准将暂降损失分为直接经济损失和间接经济损失。直接经济损失是因电压暂降对经济活动造成的人员、设备、财产的损失以及产出为废品的成本支出。间接经济损失只统计因电能质量问题使按计划本应生产出来的产品数量减少或产生次品，从而造成的利润损失，如表1。
用电压暂降严重程度和最大熵评估负荷电压暂降敏感度
第29卷第31期中国电机工程学报 V ol.29 No.31 Nov. 5, 2009 2009年11月5日 Proceedings of the CSEE ?2009 Chin.Soc.for Elec.Eng. 115 文章编号：0258-8013 (2009) 31-0115-07 中图分类号：TM 711 文献标志码：A 学科分类号：470·40 用电压暂降严重程度和最大熵 评估负荷电压暂降敏感度 肖先勇，马超，杨洪耕，李华强 (四川大学电气信息学院，四川省成都市 610065) Stochastic Estimation of Equipment Sensitivity to Voltage Sag Based on Voltage Sag Severity Index and Maximum Entropy Principle XIAO Xian-yong, MA Chao, YANG Hong-geng, LI Hua-qiang (College of Electrical Engineering and Information Technology, Sichuan University, Chengdu 610065, Sichuan Province, China) ABSTRACT: Based on physical characteristics, existing stochastic estimation methods of equipment sensitivity to voltage sag use subjective probability models to express the probability distribution of voltage tolerance curve (VTC) of equipment in the uncertain region. But the parameter estimation needs vast sample data. These methods may result in man-made errors. In order to investigate the universal rule of sensitivity estimation method, the concept of severity index was introduced and a new stochastic assessment method was proposed based on maximum entropy principle in this paper. In this method, the probability density function of VTC was determined by the maximum entropy model under limited sample data. The accumulative summing was used to calculate the failure rate of equipment during voltage sag. The estimation principle, the maximum entropy model, its constraints and the solution were investigated in detail. The approaches were also presented. As a case study, the personal computer was simulated. The simulation results compared with existing methods show that the method needs no subjective assumption under the condition of small samples and the results accord with the practical situation when the probability distribution of VTC is unknown. And this method is with good adaptability. KEY WORDS: voltage sag; equipment sensitivity; voltage sag severity; voltage tolerance curve (VTC); uncertain region; probability density function; maximum entropy principle 摘要：现有负荷敏感度随机估计法以电压暂降的物理特征为 基金项目：国家自然科学基金项目(50877049，50677041)；四川省应用基础研究项目(2008JY0043-2)。 Project Supported by National Natural Science Foundation of China (50877049, 50677041)．基础，用主观概率模型描述负荷电压耐受曲线(voltage tolerance curve，VTC)的随机分布规律，所需样本量大，在实际中难以实现且可能引入主观误差。将电压暂降特征转换为电压暂降严重性指标，在负荷VTC曲线分布规律未知和样本数较少的情况下，根据最大熵原理确定VTC曲线的概率密度函数，用累计求和法计算负荷故障率，提出一种适合于小样本的随机评估方法。对评估原理、最大熵模型、约束条件、求解算法与评估过程等进行详细研究。对个人计算机(personal computers，PC)进行仿真并与现有4种评估方法比较，结果证明，该方法对样本量依赖性小，无需主观假设，在未知VTC曲线随机分布规律时，评估结果准确，适应性强。 关键词：电压暂降；负荷敏感度；电压暂降严重性；电压耐受曲线；不确定区域；概率密度函数；最大熵原理 0 引言 随着科技和经济的发展，电网中使用敏感负荷的用户越来越多，对电能质量提出了越来越高的要求，引起了人们高度重视[1-5]。电压暂降(voltage sag 或dip)是影响用电设备正常运行的主要电能质量问题[6]。敏感负荷，如可调速电机(adjustable speed drives，ASD)、PC、可编程逻辑控制器(programmable logic controllers，PLC)和交流接触器(AC-contactor，ACC)等对电压暂降非常敏感[7-12]，单个元件故障可能引起整条生产线产品报废，造成巨大经济损失[7]。因此，准确评估敏感负荷对电压暂降的敏感度，对采取合理技术措施、降低用户风险有重要意义。 负荷电压暂降敏感度是用户设备与供电系统扰动之间的兼容性问题，受供电系统运行状态、暂降特征、负荷用电特性等诸多因素影响[13]，一般用
简单明了的告诉你—电缆线路的压降计算方法及案例
一般来说，计算线路的压降并不复杂，可按以下步骤： 1.计算线路电流I 公式：I= P/1.732×U×cosθ 其中：P—功率，用“千瓦”U—电压，单位kV cosθ—功率因素，用0.8～0.85 2 .计算线路电阻R 公式：R=ρ×L/S 其中：ρ—导体电阻率，铜芯电缆用0.01740代入，铝导体用0.0283代入 L—线路长度，用“米”代入 S—电缆的标称截面 3.计算线路压降 公式：ΔU=I×R 线路电压降最简单最实用计算方式线路压降计算公式：△U=2*I*R I：线路电流 L：线路长度。 1、电阻率ρ铜为0.018欧*㎜2/米 铝为0.028欧*㎜3/米 2、I=P/1.732*U*COS? 3、电阻R=ρ*l/s(电缆截面mm2) 4、电压降△U=IR＜5%U就达到要求了。
例：在800米外有30KW负荷，用70㎜2电缆看是否符合要 求？I=P/1.732*U*COS?=30/1.732*0.38*0.8=56.98A R=Ρl/电缆截面 =0.018*800/70=0.206欧 △U=2*IR=2*56.98*0.206=23.44>19V (5%U=0.05*380=19) 不符合要求。 2、单相电源为零、火线(2根线)才能构成电压差，三相电源是以线电压为标的，所以也为2根线。电压降可以是单根电线导体的损耗，但以前端线电压380V(线与线电压为2根线)为例，末端的电压是以前端线与线电压减末端线与线(2根线)电压降，所以，不论单相或三相，电压降计算均为2根线的 就是欧姆定律：U＝R*I 但必须要有负载电流数据、导线电阻值才能运算。铜线电阻率：ρ＝0.0172，铝线电阻率：ρ＝0.0283 例： 单相供电线路长度为100米，采用铜芯10平方电线负载功率10KW，电流约46A，求末端电压降。求单根线阻： R＝ρ×L/S＝0.0172×100/10≈0.17(Ω) 求单根线末端电压降： U＝RI＝0.17×46≈ 7.8(V) 单相供电为零、火2根导线，末端总电压降： 7.8×2＝15.6(V)
电压降计算方法
电缆电压降对于动力装置，例如发电机、变压器等配置的电力电缆，当传输距离较远时，例如900m，就应考虑电缆电压的压降”问题，否则电缆采购、安装以后，方才发觉因未考虑压降，导致设备无法正常启动，而因此造成工程损失。 一?电力线路为何会产生电压降”？ 电力线路的电压降是因为导体存在电阻。正因为此，所以不管导体采用哪种材料 （铜，铝）都会造成线路一定的电压损耗，而这种损耗（压降）不大于本身电压的 10%时一般是不会对线路的电力驱动产生后果的。 二.在哪些场合需要考虑电压降？ 一般来说，线路长度不很长的场合，由于电压降非常有限，往往可以忽略压降”的问题，例如线路只有几十米。但是，在一些较长的电力线路上如果忽略了电缆压降，电缆敷设后在启动设备可能会因电压太低，根本启动不了设备；或设备虽能启动，但处于低电压运行状态，时间长了损坏设备。 较长电力线路需要考虑压降的问题。所谓长线路”一般是指电缆线路大于500米。 对电压精度要求较高的场合也要考虑压降。 三?如何计算电力线路的压降？ 一般来说，计算线路的压降并不复杂，可按以下步骤： 1?计算线路电流I 公式：1= P/1.732 X U X cos 9 其中：P—功率，用千瓦” U—电压，单位kV cos 9—功率因素，用0.8?0.85 2 .计算线路电阻R 公式：R=pX L/S 其中：p—导体电阻率，铜芯电缆用0.01740代入，铝导体用0.0283代入 L—线路长度,用米”代入
S —电缆的标称截面 3?计算线路压降 公式：△U=I XR 举例说明： 某电力线路长度为600m，电机功率90kW，工作电压380v，电缆是70mm 2铜芯电缆，试求电压降。 解：先求线路电流I 匸P/1.732 X U X cos 9 =97J32r 关 0.380 X 0=861)) 再求线路电阻R R= pX L/S=0.01740 X 600 - 70=0.149( Q) 现在可以求线路压降了： △U=I X R =161 X 0.149=23.V9 ( 由于△ U=23.99V,已经超出电压380V的5% (23.99 -380=6.3% ,因此无法满足电压的要求。解决方案：增大电缆截面或缩短线路长度。读者可以自行计算验正。 例：在800米外有30KW负荷，用70伽2电缆看是否符合要求？ 匸P/1.732*U*COS?=30/1.732*0.38* 0.8=56.98A R= pL/S=0.018*800/70=0.206 欧 △ U=IR=56.98*0.206=11.72<19V (5%U=0.05*380=19) 符合要求。 电压降的估算 根据线路上的负荷矩，估算供电线路上的电压损失，检查线路的供电质量 2. 口诀
导线压降计算方式
解决思路： 1、已知电缆电阻率，长度，横截面积，可求出电缆电阻 2、已知电缆电阻，供电电压，可求出电缆额定电流 3、已知设备工作电流，电缆额定电流，可求出线路总电流 4、已知线路总电流，电缆电阻，可求出电缆压降 5、推导电缆压降计算总公式 详细分析： 1、电缆电阻计算 根据电阻公式：R=ρ×l/s.其中ρ为电阻率,l为长度,s为横截面积.由此便可求铜导线得电阻.注意,电阻与温度也有关系,不过这里我们一般都认为是常温.故暂不考虑温度影响. 铜的电阻率ρ=Ω．mm2/m,这个是常数. 物体电阻公式：R=ρL/S 式中： R为物体的电阻（欧姆）； ρ为物质的电阻率，单位为欧姆米（Ω.mm2/m)。 L为长度，单位为米（m） S为截面积，单位为平方米（mm2） 这样距离是L(米)的单条线缆的电阻为R（导线）=ρ*L/S 2、电流计算公式I=U/R（I表示电流、U代表电压、R代表电阻） 已知导线电阻，供电电压，求导线额定电流--I（导线）=U（12V)/R（导线） 3、集中供电各设备为并联关系，并联电路总电流等于各支路电流之和 线路总电流I（总）=I（设备1）+I（设备N）+I（导线） 4、电压计算公式U=IR
电线上的电压降等于电线中的电流与电线电阻的乘积 U（导线）=I（总）*R（导线） 5、电缆压降计算总公式 推导U（导线）=I（总）*R（导线）=【I（设备1）+I（设备N）+I（导线）】*【ρ*L/S】=【I（设备1）+I（设备N）+U（12V)/R（导线）】*【ρ*L/S】 ={I（设备1）+I（设备N）+U（12V)/【ρ*L/S】}*【ρ*L/S】 最后结论U（导线）={I（设备1）+I（设备N）+U（12V)/【ρ*L/S】}*【ρ*L/S】 考虑供电构成回路，使用的是相同的线缆。对于两条电缆来说在线路中的电压损耗是U（导线）=I（总）*R（导线），再乘以2就是实际压降。
电缆电压压降
电缆电压压降降计算公式为△U=（P*L）/(A*S) 其中：P为线路负荷；L为线路长度 A为导体材质系数（铜大概为77，铝大概为46） S为电缆截面 （一）电缆长度计算 电缆长度计算公式：L=（l+5.5G+a）×1.02 上式中， L-电缆计算长度（米）；l-按直线距离统计的长度（横纵坐标的代数和）； 5.5-穿越一个股道按5.5米长度计算，（当大于5.5米时，按实际距离计算）； G-穿越股道的股道数；a-其它附加长度，具体规定如下： 1、信号楼内的电缆储备量按5米计算，楼内走行和电缆封头的长度，一般定为20米； 2、设备每端出、入土及做头为2米； 3、室外每端环状储备量为2米（20米以下为电缆为1米）； 4、引向高出地面较大距离的设备，按实际长度计算。 1.02-电缆敷设时的自然弯曲度，以2%计算。 （二）电缆芯线分配原则 电缆芯线分配，采用双线直流回路，即一条去线ZQ，一条回线ZH。双线式回路最经济的分配比利为去线与回线等量，且均为总芯数的一半，即：ZQ=ZH=Z/2。如果电缆总芯数为奇数时，去线和回线芯数相差为一芯，这样可以使电路中芯线电阻最小。 （三）计算电缆最大控制长度 电缆最大控制长度计算公式：Lmax=△U/Ir×ZQZH/(nZQ+ZH) 式中：n-回线与去线内电流的倍数；△U-线路允许压降； I-回路中工作电流；r-每米芯线电阻。 上式表明，电缆芯线数可以通过电缆最大控制长度的计算来决定，其方法是根据线路允许压降、回路中工作电流，以及假定选用的回线和去线的电缆芯数，计算出Lmax. （四）电缆芯数计算公式 设电缆总芯数为Z=ZQ+ZH，由电缆分配原则可知ZQ+ZH,能使芯线电阻最小。所以电缆总芯线数的计算为：Z=4rL/R=4rLI/△U 上式表明：当线路允许压降△U，回路工作电流I及电缆计算长度确定之后，可以计算电缆总芯数。线路电压降计算公式为△U=（P*L）/(A*S) 其中：P为线路负荷；L为线路长度 A为导体材质系数（铜大概为77，铝大概为46）；S为电缆截面 （五）电缆线路压降计算公式 计算公式为:△U=rLI×(ZQ+ZH)/(ZQ×ZH)
电缆压降计算公式
电缆压降计算公式 线路电压降计算公式为△U=（P*L）/(A*S) 其中：P为线路负荷；L为线路长度 A为导体材质系数（铜大概为77，铝大概为46） S为电缆截面 （一）电缆长度计算 电缆长度计算公式：L=（l+5.5G+a）×1.02 上式中， L-电缆计算长度（米）；l-按直线距离统计的长度（横纵坐标的代数和）； 5.5-穿越一个股道按5.5米长度计算，（当大于5.5米时，按实际距离计算）； G-穿越股道的股道数；a-其它附加长度，具体规定如下： 1、信号楼内的电缆储备量按5米计算，楼内走行和电缆封头的长度，一般定为20米； 2、设备每端出、入土及做头为2米； 3、室外每端环状储备量为2米（20米以下为电缆为1米）； 4、引向高出地面较大距离的设备，按实际长度计算。 1.02-电缆敷设时的自然弯曲度，以2%计算。 （二）电缆芯线分配原则 电缆芯线分配，采用双线直流回路，即一条去线ZQ，一条回线ZH。双线式回路最经济的分配比利为去线与回线等量，且均为总芯数的一半，即：ZQ=ZH=Z/2。如果电缆总芯数为奇数时，去线和回线芯数相差为一芯，这样可以使电路中芯线电阻最小。 （三）计算电缆最大控制长度 电缆最大控制长度计算公式：Lmax=△U/Ir×ZQZH/(nZQ+ZH) 式中：n-回线与去线内电流的倍数；△U-线路允许压降； I-回路中工作电流；r-每米芯线电阻。 上式表明，电缆芯线数可以通过电缆最大控制长度的计算来决定，其方法是根据线路允许压降、回路中工作电流，以及假定选用的回线和去线的电缆芯数，计算出Lmax. （四）电缆芯数计算公式 设电缆总芯数为Z=ZQ+ZH，由电缆分配原则可知ZQ+ZH,能使芯线电阻最小。所以电缆总芯线数的计算为：Z=4rL/R=4rLI/△U 上式表明：当线路允许压降△U，回路工作电流I及电缆计算长度确定之后，可以计算电缆总芯数。线路电压降计算公式为△U=（P*L）/(A*S) 其中：P为线路负荷；L为线路长度 A为导体材质系数（铜大概为77，铝大概为46）；S为电缆截面 （五）电缆线路压降计算公式 计算公式为:△U=rLI×(ZQ+ZH)/(ZQ×ZH)
路灯配电缆计算公式
道路照明配电相关问题汇总： 1. YJV 电缆各规格供电半径估算： 1.1 根据电压降计算初步确定电缆截面及长度： 一般情况下道路照明供电线路长，负荷小，导线截面较小，则线路电阻要比电抗大得多，计算时可以忽略电抗的作用。又由于照明负荷的功率因数接近1，故在计算电压损失时，只需考虑线路的电阻及有功功率。由此可得计算电压损失的简化计算公式： (0.5)%p X l M U CS CS +?== 由于从配电箱引出段较短为X ，支路电缆总长为L 。则： 2%CS U L X P ?=- 对于三相供电：1500S L X P =-，对于单相供电：251.2S L X P =- P —负荷的功率，KW ； L —线路的长度，m ； X —进线电缆的长度，m ； U%—允许电压损失（CJJ45-2006-22页，正常运行情况下，照明灯具端电压应维持在额定电压的90%—105%。为了估算电缆最大供电半径取%10%U ?= ） C —电压损失计算系数(三相配电铜导线75C =,单相配电铜导线 12.56C =)
举例：假设一回路负荷计算功率为N KW，试估算不同电缆截面的供电线路长度 ?
1.2 校验路灯单相接地故障灵敏度来确定电缆最大长度： 道路照明供电线路长、负荷小、导线截面较小，则回路阻抗较大。故其末端单相短路电流较小（甚至不到100A），这样就有可能在发生单相短路故障时干线保护开关不动作。 2.路灯采用“TN-S系统”相关配电问题汇总： 2.1路灯采用“TN-S系统”单相接地故障电流计算； 下面举例对TN-S系统路灯单相接地故障进行计算： 一路灯回路长990m，光源为250W高压钠灯（自带电容补偿， =，镇流器损耗为10%）。布置间距为30m（该回路共有cosa0.85 990/30=30套灯具），采用一台100KV A的路灯专用箱变来供电，箱变内带3m长LMY—4（40X4）低压母线。采用三相配电，电缆截面为YlV—4X25+1X16。灯具引接线为BVV-3X2.5，灯杆高为10米。试计算其单相接地故障电流？
电缆截面的选择方法及计算示例
电缆截面的选择方法及计算示例 1 按长期允许载流量选择电缆截面 为了保证电缆的使用寿命，运行中的导体电缆温度应不超过规定的长期允许工作温度：聚氯乙烯绝缘电缆为70℃，交联聚乙烯绝缘电缆为90℃。根据这一原则，在选择电缆截面时，必须满足下列条件： I max ≤I 0K 式中：I max ——通过的最大连续负荷载流量（A ）； I 0 ——指定条件下的长期允许载流量（A ），见附表1； K ——长期允许载流量修正系数，见附表2. 举例：某工厂主变压器容量S 为12000KVA ，若以直埋35KV 交联电缆供电，试问应选择多大电缆截面（土壤温度最高30℃，土壤热阻系数） 解：按下列计算电缆线路应通过的电流值 I= U S 3=35 312000 ?=198（A ） 查附表1-12得：铜芯交联电缆10KV 3×95mm 2，最大连续负荷载流量为220A ，25℃。由于敷设土壤温度最高为30℃，应进行温度修正。 查附表2-2得修正系数为. I 修=220（A ）×=211（A ） 通过土壤温度的修正后该电缆的连续负荷载流量虽只有211（A ），仍能满足电缆线路198（A ）的要求。 2 按经济电流密度选择电缆截面 国际电工委员会标准IEC287-3-2/1995提出了电缆尺寸即导体截面经济最佳化的观点：电缆导体截面的选择，不仅要考虑电缆线路的初始成本，而且要同时考虑电缆在寿命期间的电能损耗成本。因此要从经济电流密度来选择电缆截面。 （1）经济电流密度计算式： J= 1000 ]201[2020?-???）（＋m B F A θαρ
（2）电缆经济电流截面计算式： S j =I max /J 式中：J——经济电流密度（A/mm2）； S j ——经济电流截面（mm2）； B=（1+Yp+Ys）(1+λ 1+λ 2 )，可取平均值； P 20———— 20℃时电缆导体电阻率（Ω·mm2/m） 铜芯为×10-9，，铝芯为31×10-9，计算时可分别取和31。 d 20———— 20℃时电缆导体的电阻温度系数（1/℃）。铜芯为，铝芯为. （3）10KV及以下电力电缆按经济电流密度选择电缆截面，宜符合下列要求： ①按照工程条件、电价、电缆成本、贴现率等计算拟选用的10KV及以下铜芯或铝PVC/XLPE 绝缘电力电缆的经济电流密度值。（详见GB 50217—2007《电力工程电缆设计规范》附录B《10KV 及以下电力电缆经济电流截面选用方法》）。 ②对备用回路的电缆，如备用的电动机回路等，宜按正常运行小时数的一半选择电缆截面。对一些长期不使用的回路，不宜按经济电流密度选择电缆截面。 ③当电缆经济截面比按热稳定、容许电压降或持续载流量要求的截面小时，则应按热稳定、 容许电压降或持续截流量较大要求的截面选择。当电缆经济截面介于电缆标称截面档次之间，可视其接近程度、选择较近一档截面，且宜偏小选取。 （4）上述计算式及要求虽然精确但比较繁杂。为方便起见，推荐下列简化的经济电流密度计算方法： 首先应知道电缆线路中年最大负荷利用时间，然后从下表中查得我国目前规定的电缆导体材料的经济电流密度，再按下式计算电缆截面。 S j = J I max 式中：I max ——最大负荷电流（A）； J——经济电流密度（A/mm2）。
电缆选型 电缆截面估算 电压降等计算
电缆选型 电缆的型号组成与顺序： 1:类别、用途2:导体3:绝缘4:内护层5:结构特征6:外护层或派生7:使用特征 1-5项和第7项用拼音字母表示，高分子材料用英文名的第位字母表示，每项可以是1-2个字母；第6项是1-3个数字。 型号中的省略原则：电线电缆产品中铜是主要使用的导体材料，故铜芯代号T省写，但裸电线及裸导体制品除外。裸电线及裸导体制品类、电力电缆类、电磁线类产品不表明大类代号，电气装备用电线电缆类和通信电缆类也不列明，但列明小类或系列代号等。 第7项是各种特殊使用场合或附加特殊使用要求的标记，在“-”后以拼音字母标记。有时为了突出该项，把此项写到最前面。如ZR-(阻燃)、NH-(耐火)、WDZ-(低烟无卤、企业标准)、-TH(湿热地区用)、FY-(防白蚁、企业标准)等。 数字标记铠装层外被层或外护套 0 无--- 1 联锁铠装纤维外被 2 双层钢带聚氯乙烯外套 3 细圆钢丝聚乙烯外套 4 粗圆钢丝 5 皱纹(轧纹)钢带 6 双铝(或铝合金)带 8 铜丝编织 9 钢丝编织 电缆的型号表示含义： 一、用途代码－不标为电力电缆，K为控制缆，P为信号缆; 二、绝缘代码－Z油浸纸，X橡胶，V聚氯乙烯，YJ交联聚乙烯 三、导体材料代码－不标为铜，L为铝; 四、内护层代码－Q铅包，L铝包，H橡套，V聚氯乙烯护套 五、派生代码－D不滴流，P干绝缘; 六、外护层代码 七、特殊产品代码－TH湿热带，TA干热带; 八、额定电压－单位KV 电缆型号选型注意事项 1、SYV：实心聚乙烯绝缘射频同轴电缆 2、SYWV(Y)：物理发泡聚乙绝缘有线电视系统电缆，视频（射频）同轴电缆（SYV、SYWV、SYFV）适用于闭路监控及有线电视工程 SYWV（Y）、SYKV 有线电视、宽带网专用电缆结构：（同轴电缆）单根无氧圆铜线+物理发泡聚乙烯（绝缘）+（锡丝+铝）+聚氯乙烯（聚乙烯） 3、信号控制电缆（RVV护套线、RVVP屏蔽线）适用于楼宇对讲、防盗报警、消防、自动抄表等工程 RVVP：铜芯聚氯乙烯绝缘屏蔽聚氯乙烯护套软电缆电压300V/300V 2-24芯 用途：仪器、仪表、对讲、监控、控制安装 4、RG：物理发泡聚乙烯绝缘接入网电缆用于同轴光纤混合网（HFC）中传输数据模拟信号 5、KVVP：聚氯乙烯护套编织屏蔽电缆用途：电器、仪表、配电装置的信号传输、控制、测量 6、RVV（227IEC52/53）聚氯乙烯绝缘软电缆用途：家用电器、小型电动工具、仪表及动力照明
电缆电压降的计算方法
电缆电压降计算方式 对于动力装置，例如发电机、变压器等配置的电力电缆，当传输距离较远时，例如900m，就应考虑电缆第一文库网电压的“压降”问题，否则电缆采购、安装以后，方才发觉因未考虑压降，导致设备无法正常启动，而因此造成工程损失。 一.电力线路为何会产生“电压降”？ 电力线路的电压降是因为导体存在电阻。正因为此，所以不管导体采用哪种材料（铜，铝）都会造成线路一定的电压损耗，而这种损耗（压降）不大于本身电压的5%时一般是不会对线路的电力驱动产生后果的。例如380V的线路，如果电压降为19V，也即电路电压不低于361V，就不会有很大的问题。 电压降△U=IR＜5%U达到要求 220*5%=11V 380*5%=19V 二.在哪些场合需要考虑电压降? 一般来说，线路长度不很长的场合，由于电压降非常有限，往往可以忽略“压降”的问题，例如线路只有几十米。但是，在一些较长的电力线路上如果忽略了电缆压降，电缆敷设后在启动设备可能会因电压太低，根本启动不了设备；或设备虽能启动，但处于低电压运行状态，时间长了损坏设备。 较长电力线路需要考虑压降的问题。所谓“长线路”一般是指电缆线路大于500米。对电压精度要求较高的场合也要考虑压降。 三.如何计算电力线路的压降？ 一般来说，计算线路的压降并不复杂，可按以下步骤： 1. 计算线路电流I 公式：I= P/1.732×U×cosθ 其中： P—功率，用“千瓦” U—电压，单位kV cosθ—功率因素，用0.8～0.85 2 .计算线路电阻R 公式：R=ρ×L/S 其中：ρ—导体电阻率，铜芯电缆用0.01740代入，铝导体用0.0283代入 L—线路长度，用“米”代入 S—电缆的标称截面 3.计算线路压降