Phase current asymmetry on the double-circuit very high voltage overhead transmission line

Tomáš Nazarčík Department of Theory of Electrical Engineering

Faculty of Electrical Engineering University of West Bohemia

Pilsen, Czech Republicnazarcik@kte.zcu.cz

Barry RawnDepartment of Electronic and Computer EngineeringCollege of Engineering, Design and Physical Sciences

Brunel University LondonUnited Kingdom

barry.rawn@brunel.ac.uk

Abstract—This paper is concerned with the calculations of the phase current asymmetry on the power vhv overhead transmission line with two circuits. Presented algorithm allows taking into consideration the mutual inductive and capacitive couplings between the conductors. Their effect can be reduced with the help of transmission line transposition. On the non-transposed transmission line these couplings cause the geometrical phase current asymmetry. The influence of the geometrical phase current asymmetry on the length of the line and on the value of transmitted power has been investigated. Total phase current asymmetry is also affected by the load asymmetry, which appears on transposed line as well as on the non-transposed one. The comparison between the transposed line and the non-transposed line with respect to asymmetrical load has been carried out.

Keywords—phase current asymmetry; double vhv transmission line; line transposition; mutual inductive and capacitive couplings; Joule losses

I. INTRODUCTION During the power transmission on the overhead

transmission lines the qualitative parameters of the electric energy the allowed limits have to be kept. These limits are given by the standards. Phase current asymmetry is one of the observed parameters. This phenomenon has been researched by many authors e.g [1],[2]. The aim of transmission system operators is to minimize the phase current asymmetry, because it causes added losses [3]. The reason is that the phase current asymmetry results in a current flowing through an earth wire and increases Joule losses. The value of phase current asymmetry can be a factor, which should be taken into account for the decision of the transmission line designer, if the transmission line should be transposed or not. The method for detailed analysis of the phase current asymmetry is published in this paper.

II. TRANSMISSION LINE MODEL

A. Transmission tower specificationsThe presented algorithm can be used for any type of the double transmission tower. In this paper the type of the transmission tower “Donau” has been considered. It carries twice three phase conductors and it has two earth wires. The design layout is depicted in the Fig.1. Phase conductor is constructed as a triple bundle conductor 3x(490-AL1/64-

Fig.1 Design layout of transmission tower Donau

ST1A), the earth wires are represented by a single conductor 185-AL1/43-ST6C.

B. Circuit model of the lineThe transmission line has been modelled as a cascade of

two-ports. Every phase conductor consists of a chain of N gamma two ports that is described in Fig.2 [4]. The basic passive line element involves a resistance, a conductance, a self-inductance and a capacitance to the earth. It is supposed that value of the resistance and the conductance are the same in the case of transposed and non-transposed line. Their values are defined according to the technical specification of conductors. The operating temperature of the phase bundle conductors is considered equal to 40°C. For this value the resistance was calculated. Value of the phase conductances was obtained from the calculation from the data obtained from the WAMS measurement of the unloaded line. The effects of the inductive and capacitive couplings between the conductors are respected via voltage and current source in every two-port. The capacitances have been determined by method of images [5], self and mutual inductances have been expressed by matrixes of inductances [6]. If we consider the harmonic steady state and linear character of the line parameters, we are able to use complex representation for voltages and currents

978-1-4673-6788-2/15/$31.00 ©2016 IEEE

This paper was supported by a project SGS-2015-035

Fig.2 Gamma two-port as the transmission line element

The voltage source represents the induced voltage via inductive couplings with other conductors. Its value for the i-th conductor can be described as:

U Lind i= ∑j=1 , j ≠i

n

jω Lij I j(1)

Number of the conductors is described with letter n. Analogously the current source expresses the induced current via capacitive with other conductors:

I Cind i= ∑j=1 , j ≠i

n

jωC ij (U i−U j ) (2)

Supposing N two-ports in each cascade and three currents in every two-port, one phase including the load has 3*N+1 unknown currents. Then three phases have 3*(3N+1) unknowns. Considering the earth wire, which two-port element does not have transverse parameters (conductance and capacitance to the earth), the number of unknowns reaches 3*(3N+1)+N. Finally the double line with two earth wires has 2(3*(3N+1)+N) unknown currents, which can be rewritten to from 20*N+6. The load is respected by resistance that is joined to the star. The solution of this equation system has been carried out in software Matlab. From the obtained load currents the phase current asymmetry can be calculated, also the Joule losses can be discovered.

For the investigations one non-transposed line and one transposed line have been considered. Phase configuration of non-transposed is described in Fig.3. The phase sequence along the transposed line with marked three transpositions is shown in Fig.4.

Fig.3 Phase configuration of the non-transposed line

Fig.4 Phase configuration of the transposed line

C. Evaluation of the phase current asymmetryIt is commonly used to express the current asymmetry via

positive and negative sequences. The load current phasors can be for this reason decomposed to sequences. The phase current asymmetry caused by asymmetric line parameters and a load asymmetry can be described by coefficients of asymmetry:

p21 =

p01 =

These coefficients are defined via rate of negative I(2) or zero I(0) and positive I(1) sequence of phase currents. With the help of these coefficients the phase current asymmetry will be evaluated in performed calculations. It is useful to evaluate the Joule losses in earth wires and describe their relation to the phase current asymmetry. Also total relative total losses Δp have been calculated [3].

III. EXAMPLES OF CALCULATIONS

For the calculations we supposed one two-port per 1 km of the length of the transmission line. In this case the transmission line model properties are similar to the model of transmission line with distributed parameters. For the calculations the symmetrical voltage source has been considered. The origin of the Joule losses in the earth wires is a consequence of phase current asymmetry. Their evaluation gives useful information about current distribution in the observed system.

A. Geometrical phase current asymmetry on non-transposed lineMutual inductive and capacitive couplings due the

different geometrical positions of conductors cause the phase current asymmetry. The effects of the couplings depend on some factors, which have been investigated further.

1) Phase current asymmetry dependency on the length of the line

The value of transmitted was considered equal to 1200 MW for both circuits together. The calculations have been performed for discrete values of the transmission line length in the interval from 50 to 130 km. Results for chosen length are described in table I., the dependency of Joule losses of earth wires is shown in Fig. 5. Numbers I. and II. mean the index of the first and second circuit of the double line.

Fig.5 Dependency of Joule losses of earth wires on the line length

TABLE I. PARAMETERS DEPENDENCY ON THE VARIABLE LINE LENGTH FOR 1200 MW OF TRANSMITTED POWER

The results in table have shown that with increasing line length increase the phase current asymmetry of both circuits. The increment of the zero sequence of current has linear tendency. The increase in Joule losses of earth wires has quadratic trend.

2) Phase current asymmetry dependency on the value of transmitted power

For the calculations it was considered a fixed length of the transmission line equal to 100 km. The range of observed change of transmitted power was between 200 and 2000 MW for both circuits together. Results for chosen values of transmitted power are described in table II., the dependency of Joule losses of earth wires is shown in Fig. 6

Fig.6 Dependency of Joule losses of earth wires on transmitted power

TABLE II. PARAMETERS DEPENDENCY ON THE VARIABLE TRANSMITTED POWER FOR 100 KM LINE LENGTH

The increase in zero sequence as well as in negative sequence is linear. Under the value of transmitted power equal to 800 MW, the Joule losses of earth wires are small. Above this value they rise rapidly. We can also observe the increase in total relative losses with the higher value of transmitted power.

B. Influence of the asymmetrical load on the phase current asymmetry on the transposed line

Transmission line transposition allows reducing phase current asymmetry caused by inductive and capacitive couplings. The origin of the phase current asymmetry on the transposed line is caused because of asymmetrical load, source or both. The sensitivity analysis, how the transposed line reacts on the load asymmetry, has been carried out. It was considered the change of the value load power of the same phase in both circuits, which is in the model represented by the change of the value of load resistance. The performed calculations have shown that the difference in results depending on the position of the asymmetry can be on transposed line neglected. For the calculations the length of the line was supposed to be equal to 100 km. The value of transmitted power has been considered equal to 1200 MW. The results of coefficients of asymmetry are shown in table III.

TABLE III. PARAMETERS DEPENDENCY ON THE VARIABLE LOAD ASYMMETRY FOR 1200 MW OF TRANSMITTED POWER AND 100 KM LINE

LENGTH

Line length 50 km 70 km 90 km 110 km 130 km

CircuitI.

p21 0,049 0,075 0,107 0,143 0,184

p01 0,698 0,983 1,268 1,555 1,842

CircuitII.

p21 0,485 0,681 0,878 1,076 1,275

p01 0,378 0,528 0,677 0,824 0,970

ΔPje [kW] 2,79 7,748 16,621 30,574 50,769

Δp [%] 0,4201 0,5904 0,762 0,9437 1,1085

Load asymmetry 1 % 2 % 3 % 4 % 5 %

CircuitI.

p21 0,331 0,667 1,007 1,352 1,702

p01 0,329 0,662 0,999 1,341 1,688

CircuitII.

p21 0,331 0,666 1,005 1,35 1,7

p01 0,329 0,662 0,999 1,341 1,688

ΔPje [kW] 2,325 9,425 21,495 38,734 61,353

Δp [%] 0,84 0,84 0,841 0,843 0,845

Transmitted Power [MW] 200 650 1100 1550 2000

CircuitI.

p21 0,06 0,087 0,117 0,148 0,179

p01 0,241 0,758 1,291 1,839 2,404

CircuitII.

p21 0,157 0,521 0,893 1,276 1,674

p01 0,131 0,410 0,689 0,967 1,246

ΔPje [kW] 0,375 1,319 15,508 70,466 212,995

Δp [%] 0,3603 0,5001 0,7809 1,0943 1,4349

Fig.7 Dependency of zero sequence of current on the load asymmetry

The results have shown a linear increasing tendency of negative and zero sequence of current. The trend of the increase in the Joule losses of earth wires is quadratic. The relative losses do not change significantly.

C. Load asymmetry on the non-transposed line

Performed calculations described in tables I and II have shown that the phase current asymmetry depends on the length of the line as well as on the value of transmitted power. The total phase current asymmetry on the non-transposed line is also affected by asymmetrical load. This fact is shown in this subsection. The asymmetrical load is as well as in subsection B represented by a change of load power. This situation has been modeled as a decrease of resistance by 2% in one phase of both circuits. Contrary to the transposed line, on the non-transposed line it matters, in which phase the load asymmetry is. The total phase current asymmetry is the consequence of the geometrical asymmetry of non-transposed line and the asymmetry of the load at the same time. If we consider parallel operating of both circuits, there exist three possibilities of the load asymmetry (in each phase). All of them have been calculated and the results are shown in table V. For the performed calculations the value of transmitted power has been considered equal to 1200 MW and the line length equal to 100 km. The cases of load asymmetry are depicted in table IV.

TABLE IV. CONSIDERED CASES OF LOAD ASYMMETRY

TABLE V. COEFFITIENS OF ASYMMETRY, JOULE LOSSES AND RELATIVE LOSSES FOR ASYMETRICAL LOAD AND 1200 MW OF TRANSMITTED POWER

D. Zero sequence of current on the and non-transposed transmission line

If we declare the allowed value of p01 (coefficient of asymmetry for zero sequence) equal to 2 %, we can make an investigation of dependency of permitted p01 on both parameters (line length and transmitted power). For chosen discrete values of line length it was calculated the critical transmitted power, which causes at least on one of considered circuits the p01 equal to 2%. The dependency is shown in Fig. 8. Firstly it is shown the curve in the case of non-transposed line with the symmetrical source and load. Then there are displayed the results for the load asymmetry in phase b on non-transposed line, which provide according to the table V worst results for the zero sequence. The decrease in load resistance is 2%. Additionally it is shown the limit curve for the non-transposed line with asymmetrical load with same position of asymmetry (phase b), but with the decrease of load resistance by 3%.

Fig.8 Limit curves for p01 on non-transposed line

The limit curves have the hyperbolic shape and they show an allowed area, where the zero sequence of current does not exceed the predefined permitted value.

Load phase a1 b1 c1 a2 b2 c2

1. case X X

2. case X X

3. case X X

Load asymmetry phase a phase b phase c

CircuitI.

p21 0,788 0,565 0,68

p01 1,265 2,063 1,199

CircuitII.

p21 1,594 1,183 0,503

p01 1,373 0,399 0,977

ΔPje [kW] 34,622 42,082 20,490

Δp [%] 0,850 0,850 0,848

IV. CONCLUSION

This paper described a method which allows evaluating the phase current asymmetry on the double vhv transmission line. This algorithm takes into account the mutual inductive and capacitive couplings, which have an impact on the geometrical phase current asymmetry. The geometrical phase current asymmetry dependency on the line length and on the value of transmitted power has been investigated. The influence of asymmetrical load on the asymmetry has been researched for transposed as well as for non-transposed line. The total phase current asymmetry on non-transposed line is a consequence of the geometrical and load asymmetry. Obtained results have shown that the load asymmetry can intensify the geometrical phase current asymmetry. In other phase configuration the geometrical and load asymmetry can compensate themselves. Joule losses of the earth wires correspond to the values of zero sequences of current of both circuits. From the point view of electricity qualitative parameters the phase current asymmetry can be a limited factor. The decision, if the transmission should be transposed or not, should take into account not only the line length, also the value of transmitted power too.

ACKNOLEDGEMENT

The authors would like to thank the company ČEPS a.s. for providing data of technical specification of transmission towers.

REFERENCES

[1] Hesse, M.H.; Sabath, J., "EHV Double-Circuit Untransposed Transmission Line-Analysis and Tests," in Power Apparatus and Systems, IEEE Transactions on , vol.PAS-90, no.3, pp.984-992, May 1971

[2] H. Holley, D. Coleman and R.B. Shipley: “Untransposed EHV Line Computation”, Power Apparatus and Systems, IEEE Transactions on,vol.83 1964

[3] T. Nazarčík, Z. Benešová,” Comparison of Joule’s losses on transposed and non-transposed transmission line”, 16th conference on Electric Power Engineering (EPE 2015), Kouty nad Desnou 2015

[4] A. Novitskiy, D. Westermann, “Interaction of Multi-Circuit Overhead Transmission Lines of Different Voltages Located on the Same Pylon” Electric Power Quality and Supply Reliability Conference (PQ), 2012

[5] Z. Benešová, L. Šroubová,”Capacitive Coupling in Double-Circuit Transmission Lines”, Advances in Electrical and Electronic Engineering, Žilina 2004

[6] Z. Benešová, D. Mayer, “Algorithm for Computation of Inductances of Three/phase Overhead Lines”, AMTEE’03 Pilsen, UWB in Pilsen 2003