Zakariya M. Al-HamouzDepartment of Electrical Engineering

King Fahd University of Petroleum and MineralsDhahran 31261, Saudi Arabia

Email: zhamouz@kfupm.edu.sa

Abstract: A comparison between the corona power loss associated with HVDC transmission lines and the lineohmic power loss is presented in this paper. The work is aimed at pointing out that the general trend ofneglecting the corona power is not always valid. The comparison demonstrates the percentage of the coronapower loss to the ohmic power loss when the transmission line is heavily (100% loaded), moderately (75%loaded) and lightly (50% loaded) loaded. It has been found that when the line is moderately or lightly loaded,this percentage could reach more than 100% especially when the line is going deep in corona (the operatingvoltage is equal or greater than 1.5 the corona onset voltage).

1. Introduction

In transmission networks planning, there is anongoing interest on obtaining the most economicalconfiguration that satisfies all pre-specifiedconstraints. In this regard, economy includes theinvestment cost as well as the operational cost. Inthe literature, it has been reported that one of thefactor that highly affects the amount of theoperational cost is the transmission line ohmicpower loss [1].In high voltage transmission lines (AC or DC) andwhen the applied voltage exceeds a value named"onset voltage", the very thin layer of air around thetransmission line ionizes. This ionization processresults in corona power loss, radio interference andaudible noise [2]. In many attempts reported in theliterature, the contribution of the corona power lossto the total transmission line power loss is claimedto be low and therefore has been neglected [1].Many factors affect the "onset voltage" of atransmission line and hence the corona power lossassociated with it. Among theses factors are theconductor radius, conductor smoothness (roughnessfactor), number of bundles, spacing of bundles,height and the weather conditions (humidity, rain,snow and wind). In this paper, the author attemptsto present the importance of the corona power lossand its significant value as compared to thetransmission line ohmic power loss. Theinvestigation includes both fair and rainy conditionsfor laboratory scale DC transmission lines.2. Numerical and Experimental

Evaluation of Corona Power Loss

2.1 Numerical evaluationThe equations that constitute the mathematicaldescription of the monopolar ionized field in airare:

=rE r e/ 0 (1)

=rJ 0 (2)r r

J E= mr (3)rE = -j (4)

where e0 is the permittivity of free space and m isthe ion mobility.Equations (1)-(4) are respectively Poissonsequation, the current continuity condition, theequation of current density and the equationrelating the electric field to the potential. Thesepartial differential equations are coupled nonlinearin nature and hence have no analytical solutionexcept for simple geometries such as spherical andcoaxial configurations [3]. In the present paper, thefinite element method (FEM) based algorithmdeveloped before by the author [4] is used toanalyze the monopolar ionized field on bundledconductors and hence estimate the associatedcorona power loss.For each applied voltage above the corona onsetvalue, the total corona current is

= =

=NB

k

M

iikik AJI

1 11, (5)

where NB is the number of bundles, Aik ,1 is the perunit cross sectional area of the ith flux tube at thesurface of the kth bundle and Jik is thecorresponding per unit current density at thatbundle surface. Therefore, the corona power loss(kW/km) at any applied voltage V is equal to

IVPcorona = (6)It is worth mentioning that numerical computationof the corona current under rainy conditions isextremely difficult especially for bundled conductortransmission lines. Hence, for the case of rainyconditions, only experimental results are presented.

2.2 Experimental evaluationAn experimental set-up has been designed andconstructed at the high voltage laboratory of KingFahd University of Petroleum and Minerals. Theset-up is designed in a way to enable corona currentmeasurement under fair and continuous rainyconditions. Also, the design made it possible tovary the transmission line number of bundles,height, radius, orientation and bundle spacing. Thetwo ends of each bundle were terminated byspherical caps in order to prevent corona fromtaking place at these ends. The tested transmissionlines consist of different groups of smoothedbundles.

3. Evaluation of Ohmic Power Loss

The ohmic power loss (kW/km) for a certaintransmission line configuration is computed fromequation 7:

RInP cohmic2)(a= (7)

where:n is the number of bundles,

cI is the current carrying capacity of thebundle,

R is the transmission line resistance.a is the line loading factor (taken as 1, 0.75

and 0.5 in the present study)

For different conductor radii, the current carryingcapacity is determined using the Schring and Frickformula [5].

4. Results and Discussion

The corona power loss and ohmic power loss weremeasured and computed for different transmissionline configurations (bundles 1, 2, and 3) and underfair and rainy conditions, Fig. 1.

For a transmission line with smoothed singlealuminum conductor (R= 0.125 cm, H= 54.5 cm),the percentage ratio of the corona power loss to the

ohmic power loss ( ohmiccorona PP / ) at fair weatherconditions is plotted in Fig. 2 for different loadingconditions of the transmission line (50%, 75% and100% loading). It is clear that as the transmissionline becomes lightly loaded, the ratio

ohmiccorona PP / increases and may reach 100%especially if the line is operating at a voltage wellabove the corona onset value (which is 46 kV forthis configuration). Of course, this demonstrates theimportance of the corona power loss as comparedto the ohmic power loss. This percentage increasessubstantially under rainy conditions. This isdemonstrated in Fig. 3 for horizontal bundle 2transmission line of H= 77 cm, R= 0.01 cm and S=6 cm when operating at 50% line loading. It isworth mentioning that under rainy conditions, themeasured corona power loss values vary between aminimum and a maximum vale for each appliedvoltage. Therefore, in figure 3, the average valuesof the corona power loss were used to compute theratio ohmiccorona PP / . It is quite clear that underrainy conditions corona starts much earlier than inthe case of non rainy conditions. This is due to thefact that rain droplets on the transmission lineconductors can be viewed as sharp edges whichenhances the electric field and therefore reduces thecorona onset voltage and hence increases thecorona power loss.

S

R

Ground Plane

12

n

H

Fig.1: n-bundle transmission line configuration(n=3 in the present case)

020

40

60

80

100

120

45 55 65 75 85Applied Voltage (kV)

(Pco

ron

a/P

oh

mic

) x10

0%

50% Loading75% Loading100% Loading

Fig. 2: Corona power loss as a percentage of ohmicpower loss

The effect of varying the number of conductors onthe ohmiccorona PP / ratio for a selected transmissionline loading of 50% is demonstrated in Fig. 4. It canbe seen that as the number of bundles increases, theratio decreases. This can be attributed to the factthat as the number of bundles increases, the coronapower loss decreases and at the same time theohmic power loss increases. Therefore, the overall

ohmiccorona PP / ratio decreases.

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100

Applied Voltage (kV)

(Pco

ron

a/P

oh

mic

)x10

0% No Rain

Rain

Fig.3: Effect of rain on enhancing the

ohmiccorona PP / ratio for bundle 2 transmission line

5. Conclusions

The contribution of the corona power lossassociated with HVDC transmission lines to theohmic power loss has been studied in this paper.This study investigated this contribution underheavily, moderately and lightly loaded transmissionlines. Also the effect of rainy conditions on thiscontribution has been investigated for bundlestransmission lines. It has been found that underlightly loading conditions, the ratio of the coronapower loss to the ohmic power loss is high and may

reach 100% if the line is going deep into corona. Inaddition, It has been found that this ratio decreaseswith the increase in the number of bundles. Finally,it has been found that this ratio increasessubstantially under rainy conditions.

0

20

40

60

80

100

40 50 60 70 80

Applied Voltage (kV)

(Pco

ron

a/P

oh

mic

)x10

0% bundle 1bundle 2bundle 3

Fig. 4: The effect of number of bundles on the ratioof corona power loss to the ohmic power loss

References

[1] T. Gonen, Electric Power TransmissionSystem Engineering: Analysis and Design,Johm Wiley & Sons, 1988.

[2] EPRI, Transmission Line Reference Book:345kV and Above, 1975.

[3] M. Khalifa, High Voltage Engineering-Theary and Practice, ed. M. Khalifa,Marcel Dekker, 1990.

[4] Z. Al-Hamouz, "Combined Finite Element- Charge Simulation Computation ofMonopolar Corona on Bundle Wires", 33rd

IEEE Industry Application AnnualConference, St. Louis, Missouri, USA, pp.1988-1993, October 1998.

[5] Westinghouse Electric Corporation,Electrical Transmission and DistributionReference Book, 1950/

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