osman 2014
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Benefits of Optimal Size Conductor in Transmission systemTRANSCRIPT
Benefits of Optimal Size Conductor in Transmission System
Ilham Osman Department of Electrical and Electronic Engineering
Primeasia University Dhaka, Bangladesh
Mir Ashikur Rahman Department of Electrical and Electronic Engineering
Bangladesh University of Engineering and Technology Dhaka, Bangladesh
Ahmed Rayhan Mahbub Department of Electrical and Electronic Engineering
Primeasia University Dhaka, Bangladesh
Ariful Haque Dept. of Physics, Astronomy and Material Science
Missouri State University Missouri, United States
Abstract— Millions of kilowatt-hours of energy is continuously transferred from generation end to load end through transmission lines. Lower transmission loss in a power system increases the transmission efficiency and reduces the unit cost of electricity. This loss is generally reduced either by increasing the transmission voltage and or decreasing the resistance of the transmission conductor. The decrease of resistance usually increases the volume of the material incurring a higher cost. This paper proposes a cost model with a view to evaluate the optimal conductor size for a given voltage level in the transmission sector of a power system. The optimization model is applied to Bangladesh Power system (BPS) to evaluate the optimal conductor size for each of its existing lines. Comparing the losses the annual benefits of the use of optimal conductor is also evaluated. The evaluated results show that the selection of the conductor size for the transmission system requires careful attention.
Keywords— Optimal conductor size, Corona loss, Bangladesh Power System, ACSR conductors and Cost model for transmission system.
I. INTRODUCTION Electricity is produced in the generation sector to supply to
the consumers through distribution sector. The transmission sector is introduced between generation and distribution sectors to reduce the loss in carrying electricity from the generation end to the distribution end. The investigation of the Department of Energy of USA [1] shows that the loss in the transmission and distribution sectors of the country in 2011 is 7.1% of its total electricity use in the states. The worth of this amount of national annual loss is $28.8 billion.
The transmission loss is reduced by increasing the transmission voltage and also by decreasing the resistance of the transmission line conductor. Both of these two loss reducing factors require higher capital investment.
Kennon et. al.[2] consider a range of line optimization techniques which can be applied to decide whether standard or
optimized line designs are appropriate. They observed that even simple methods of optimization can help the designer keep the costs to a minimum. In [3], Eghbal et.al. introduces an optimization approach to determine the optimal voltage level. The paper considers cost associated with overhead conductors, shunt and series power compensation and active power losses to obtain an optimal voltage level. Like [2],[3] most of the optimization approaches solve the problem of voltage level and conductor size together. However, in a utility optimal transmission voltage level/levels are determined considering its global perspective. For a particular transmission line, especially for the short length line, the voltage level is decided considering one of the grid voltage levels. The problem is then to determine the optimal conductor size.
This paper proposes a simple optimization approach to determine the optimal conductor size for a given transmission line. The approach is based on a cost model which includes both copper and corona losses. The model is proposed with a view to help designer determine the optimal size of the conductor where the voltage level is already decided. The proposed model is applied to BPS to determine the optimal conductor size for each of the line of BPS. The reduction of loss and the corresponding economic benefits are evaluated. The results are encouraging and deserve the attention of the transmission line designers.
II. METHODOLOGY During the transfer of electrical energy from the generation
sector to the distribution sector through transmission lines a portion of the energy is lost in the transmission lines. This loss has two components :
i) Copper loss and ii) Corona loss
The manifestation of these losses is the production of heat. The excessive heat limits the flow of electrical power through the transmission line, commonly known as the thermal limit.
The copper loss is expressed in terms of the amount of current, I, flowing through the transmission line and the resistance, R of the line as
P cu loss= I2 R (1)
Where, P cu loss= Power loss in each phase of the transmission line(watt) I = Phase current (Amp) R = Resistance of each phase (ohm).
Corona loss is caused by the ionization of air molecules around the transmission line conductors. The formation of corona is noticed by hissing noise, the smell of ozone and the glow. Along with other factors, these noticeable parameters are dependent on weather condition. The corona loss is expressed by an empirical formula [4] as :
P Corona loss = (f+25) √ (Vph – Vdo) x 10-2 (2)
Where, Pcorona loss=Power loss in each phase of the transmission line per km (watt/km).
δ = Normalized air density factor. f= Frequency. r= Radius of the conductor (cm). d= Spacing between phases (cm). Vph = Phase voltage (line to neutral) (kv). V do = Disruptive critical voltage (kv).
The disruptive critical voltage, Vd0, of equation (2) depends on the geometry of the conductor and weather condition and initial voltage at which corona starts to form. This voltage may be expressed as-
⎟⎟⎠
⎞⎜⎜⎝
⎛∗∗=
rDed rmgV log**000 δ
(3) Where,
g0 = Disruptive gradient in air (kv/cm). m0= Roughness factor of the conductor. D = GMD equivalent spacing between conductors (cm).
Although, the power loss component P cu loss linearly varies with the resistance of the conductor for a given amount of current flow, however, P Corona loss is complex in nature. To observe the dependence of these two losses on the size of the conductor, the variation of these two with the variation of conductor resistance are separately depicted in Fig.1 for a typical line of 230 kv and 1000 km long.
Fig. 1 Variation of Cu loss and Corona loss with the size of the conductor.
Note that the increased or the decreased diameter of the conductor increases or decreases the volume of the material for the conductor and it has a clear reflection in the cost of transmission. The transmission loss as a whole, copper and corona loss together, and the cost of the conductor for the line considered in Fig.1 are depicted for the different size of the conductors in Fig.2.
Fig. 2 Variation of transmission loss and the corresponding cost of conductor for a 1000km line.
Fig.2 clearly reveals that the decrease of transmission loss requires the increased investment in transmission line. The figure also reveals that an optimal condition, M, may be obtained. This optimal condition may not be unique for each line. In order to evaluate an optimal condition in terms of conductor size a cost function is proposed in what follows :
J(R) = JA + JB (4)
JA of equation (4) is the cost due to the transmission loss and it may be expressed as :
JA = η1 [ I2 R + (f+25) √ (Vph – Vdo) x 10-2 ] (5)
Where, η1 is the cost per unit of energy loss.
The second term JB of equation (4) is the conductor cost and may be expressed as :
JB = η2 (π r2 l ρ) (6)
Where, η2 =cost/unit volume of conductor material. l = length of transmission line (km). ρ = density of the material / unit volume (gm/cm3).
To obtain the optimal diameter of the conductor the cost J(R) should be minimized for the rated condition of the power flow. That is :
Min {J(R)} such that Ploss + Pflow = PR (7)
where, Ploss = P cu loss + Pcorona loss Pflow = Vph I cos ∠ Vph , I PR = Rated power flow per phase through the line.
III. RESULTS A. Evaluation of optimal conductor size and benefits of its use :
The cost model developed in section II is applied to BPS with a view to observe its applicability and also to evaluate the benefits of the use of optimal conductors in transmission lines.
The BPS transmission sector is an integrated grid of two
voltage level transmission lines; 132 and 230 kv. Extra high voltage line is not economical for BPS as the grid network consists of comparatively small geographical area and it does not transfer huge electrical power. The 400kv transmission lines are under construction, which will raise transmission voltage level of this grid from two to three. The statistics of BPS grid in terms of voltage level and line length are presented in Table 1 [5]. The line length is expressed in terms of the distance of the circuit. For example, for a double circuit line, the length of the circuit is twice the actual distance.
TABLE I
TRANSMISSION LINE STATISTICS OF BPS.
Voltage Level (kv) No. of lines Total line length (in ckt km)
132 80 6071.34
230 20 2647.30
400 3 686.00
Out of 103 transmission lines, 3 (three) lines are randomly selected and they are described in Table II. All of these three lines are made of aluminum with steel re-inforced.
TABLE II DIFFERENT PARAMETERS OF SELECTED LINES :
Location
Conductor
Lin
e L
engt
h (k
m)
Vol
tage
Lev
el (k
v)
Cur
rent
car
ryin
g ca
paci
ty (A
mp)
Usu
al P
ower
flow
(M
W)
From To Type
Tongi Ghorasal Grosbeak 27 230 753 123.3
Shahji bazar
Chatak Grosbeak 150 132 600 237.6
Comilla North
Meghna Ghat
Twin Mallard
56 230 1500 345
Using the cost function of section II, the optimal conductor size is evaluated for each of the selected lines. The evaluation process considers the price of aluminum as $1.14/lb. The variation of the cost J(R) with the variation of the diameter of the conductor for all these lines are depicted in Figure.3 :
Fig. 3 Variation of cost with the variation of conductor size.
The evaluated optimal conductor size and the corresponding power losses are compared with the existing values in Table III. The table also presents the annual saving for each of the selected lines. The unit cost of electrical energy is considered as Tk. 2.60/KWhr.
The table reveals that the annual saving with the optimal conductor depends on the voltage level and also on the type of conductor. Note that the corona loss is a function of voltage and the copper loss increases with the increase of conductor resistance.
TABLE III COMPARISON BETWEEN THE EXISTING LINE LOSS WITH THE EXPECTED ONE FOR LINES WITH OPTIMAL CONDUCTOR SIZE
Location Conductor diameter
(cm)
Line loss (MW)
Annual Savings (Tk.x 105)
From To
Exi
sting
(cm
)
Opt
imal
(cm
)
For
exi
sting
For
opt
imal
co
nduc
tor
Total
Saving
/ km
Tongi Ghorasal 2.264 2.22 3.22 2.52 15.01 0.55
Shahji bazar
Chatak 2.025 2.00 6.39 6.378 122.5 0.816
Comilla North
M.Ghat 2.264 *2
3.37 5.38 5.074 69.6 1.244
The paper also investigates the optimal conductor size for
each of the line of BPS. However, the optimal size of conductor for 11 lines of 132kv and one line of 230kv are not possible to determine as the necessary data are not available. In this case, it is considered that the existing line is replaced by ACSR conductor of optimal diameter. The evaluated result is presented in Table IV.
TABLE IV COMPARISON OF LOSSES OF EXISTING AND OPTIMAL
CONDUCTORS AND THE CORRESPONDING ANNUAL BENEFIT Voltage Level (kv)
No. of lines
Line length (km)
Hourly total loss (MWhr)
Annual saving
(Tk x107) Existing
conductor With
optimal ACSR
conductor 132 69 3360.8 143.23 131.02 27.84 230 19 1324.4 117.32 95.178 50.43
The reduction of line loss due to the use of optimal conductor is shown in Fig.4. Saving per unit length of line for both 132 and 230 kv lines are depicted in Fig.5.
Fig.4 Reduction in line loss due to optimal conductor size.
Fig.5 Annual saving per unit length of conductor when optimal size is used.
Table IV and Fig.5 show that the saving in case of 230kv lines is more than that of 132kv line. Similarly, the reduction in line loss in 230kv lines is more than that of 132kv lines.
During the investigation it appears that in many lines of 132kv, the existing conductor size is close to the optimal. However, in case of conductors of 230kv lines, a significant difference is observed when the optimal size is compared with the existing one. Moreover, the consideration of corona loss in the optimization model creates a significant difference in 230kv lines as this loss increases with the increasing voltage level.
IV. CONCLUSION The selection of optimal conductor size in the transmission
sector reduces the transmission loss resulting lower cost of electricity. This paper develops a simple optimization model based on a cost function appropriate for transmission system with a view to help designer select conductor size for a given voltage level. The model is applied to each of the line of BPS and optimal conductor size for each line is evaluated. The annual losses for each line and also for the global system (BPS) are evaluated. The corresponding expected annual savings due to the use of optimal conductor is determined. The evaluated result clearly reveals that the optimal conductor size reduces a significant amount of transmission loss creating an eloquent annual saving. The benefits in terms of the reduction of line loss or reduction of the cost of electricity are more for higher voltage transmission lines.
REFERENCES [1] "State Electricity Profiles 2011", US Energy Information
Administration, DOE/EIA 0348(01)/2, July 2012. [2] Kennon, R. E., & Douglass, D. A. (1990). EHV transmission line design
opportunities for cost reduction. Power Delivery, IEEE Transactions on, 5(2), 1145-1152.
[3] Eghbal, M., Saha, T. K., & Nguyen, M. H. (2010, December). Optimal voltage level and line bundling for transmission lines. In Universities Power Engineering Conference (AUPEC), 2010 20th Australasian (pp. 1-6). IEEE.
[4] Peek, F. W. (1911). The law of corona and the dielectric strength of air.American Institute of Electrical Engineers, Transactions of the, 30(3), 1889-1965.
[5] (2012) List of Transmission lines, PGCB Official website [Online]. Available: http://www.pgcb.org.bd/index.php?option=com_content&view=article&id=288&Itemid=207