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Study of power flow and transmission capacity in multi phase transmission lines
1.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING TECHNOLOGY (IJEET) ISSN 0976 – 6545(Print) ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME: www.iaeme.com/IJEET.asp Journal Impact Factor (2014): 6.8310 (Calculated by GISI) www.jifactor.com IJEET © I A E M E STUDY OF POWER FLOW AND TRANSMISSION CAPACITY IN MULTI PHASE TRANSMISSION LINES Vinay Kumar Tripathi, Anil Kumar Bharadwaj Department of Electrical Engineering, SHIATS, Allahabad 43 ABSTRACT There are many problems regarding power flow and stability is an issue of vital importance at EHV (Extra High Voltage) and UHV (Ultra High Voltage) level because of its sensitivity with real and reactive power changes. An investigation of multiphase system has been carried out in this paper by extending the techniques of three-phase systems to multi-phase lines and construction of performance characteristic curves relating to power flow and voltage stability performance of such system. A comparison of multiphase phase systems is presented in the paper that can be used for planning, development and design of multiphase transmission network Keywords: Transmission Lines, Rights-of-Way, Multi-Phase, Power Flow. I. INTRODUCTION The contemporary power system network has of load and power flow conditions leading to problems of line capacity. In this regard multiphase power transmission systems have been investigated [1]- [9] as potential alternative to increase transmission capacity without increasing system voltages. The system voltage has already reached extremely high level i.e. EHV and UHV and it has been found that 4-phase and 12-phase are quite promising. The problems concerning power flow and stability, particularly voltage stability are of particular interest because of its sensitivity with changes in real and reactive power. Voltage stability is obtained by keeping specified voltage magnitude within the set of operating limits under steady state conditions. The problem has been studied to a great extent in case of three-phase systems [10]-[19]. However the multiphase system has received little attention and needs similar study. This paper deals with investigation of these aspects by using techniques of three-phase systems to multi-phase lines. A number of performance characteristic curves have been obtained relating to power flow and voltage stability of such system. Considering the multi-phase line as longitudinal or radial or the one linking to systems on either end, several performance characteristics such as, (i) reactive power requirements characteristics, (ii) reactive power loss characteristics, (iii) voltage power characteristics (under
2.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME loading conditions), (iv) load end real and reactive power operating contour maps, (v) shunt capacitive support at voltage stability limit using characteristic of voltage dependant load, and (vi) optimal reactive power at voltage stability limit, loadability curves can be constructed as done in [22] Employing a sample system a quantitative as well as qualitative analysis is carried out to highlight relative performances of such systems as compared to their three phase counterparts. Such performance curves would be highly helpful in planning and evaluating performance of multi-phase. The paper is organized as follows: Various performance characteristics for multiphase transmission system have been derived and graphically analyzed in section III to compare the advantages and limitations of multiphase system with conventional three phase system. The analysis of reactive power requirement for voltage stability of multiphase and three phase system has been carried out in section IV. Loadabilty analysis of multiphase system with compensator has been reported in section V. II. BASIC CIRCUIT MODEL AND SAMPLE SYSTEM The basic circuit model with lumped parameters adopted for the appropriate characteristics analysis of un-compensated EHV power transmission system is represented on single phase equivalent basis as shown in Fig. 1. Let EA and IA represent the voltage and current at sending end whereas EB and IB are the voltage and currents at receiving end side. YT and YSH in Fig. 1 represent equivalent series and shunt admittance of an equivalent pi-model of the transmission line. Figure (1): basic circuit model For performance evolution three transmission alternatives (3, 4 and 12-phase) with same number of conductors, same right of way and utilization of the same air space for power transmission are considered. Each system is energized at 460 kV line-to ground (L-G) voltages and has the same thermal rating. The line-parameters are based on assumptions of complete transposition of conductors are depicted in Table 1. TABLE I: TEST SYSTEM SPECIFICATION LINE PARAMETERS 44 III. PERFORMANCE CHARACTERISTICS A. Load End Real and Reactive Power Operating Contour Maps With reference to Fig.1, load end real and reactive power operating contour maps [14] can be described by the following expression. | | | | | * 2 * B BB B BB B S −Y E = eY E (1)
3.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME The above equation is an equation of a circle with | | * 2 45 BB B Y E as centre and | | * * BB B e Y E as its radius. Thus all states having the constant amplitudes of e (=EAYBA/YBB) lie on the circles with these parameters on the S-plane (Fig. 2). Each circle (Fig. 2) represents the locus of |SB|,the receiving end complex power, for a stable value of EB (receiving end voltage), varying within the range of 0.94 p. u. to 1.0 p. u. that assuming sending end voltage EA to be constant at 1.0 p.u., the load end real and reactive power operating contour maps, for 3, 4 and 12-phase are constructed for 460 kV and 200 km transmission lines, on p.u. basis, are shown in Fig. 2. It is evident from the curves in Fig. 2 that the power handling capacity of multi-phase (employing more than 3-phase) transmission system is higher for specified sending end and receiving end voltages while maintaining the similar nature of variation. Fig.2: Real reactive power operating contours with same receiving end voltages (EB = 0.94 p. u.) Furthermore, Figure 3 (a-c) confirm enhancement of power handling capacity for 3, 4 and 12- phase transmission system with 4% increase of receiving end voltage EB1 = 0.94, EB2 = 0.95 and EB3 = 1.0 p.u. maintaining sending end voltage (EA) as it is i.e. EA = 1.0 p.u. It is observed that reactive and real power handling capacity for 3-phase, 4-phase and 12-phase systems are increased by 10.80 %, 7.30 %, 6.70 % and 4 %, 3.340% %, 3.380 % respectively. As supplement, it can be seen from Figs. 3(a-c) that increment in real and reactive power capacity for 3-phase, 4-phase and 12-phase takes place with an increase of 9 % in EB (within voltage stable zone) keeping EA constant at its previous value i.e. EA=1.0 p.u.. It is observed that the corresponding percentage increase of in real and reactive power capacity of 3-phase, 4-phase and 12-phase are found to be 9, 8.66, 8.63 and 16.31, 12.77 and 14.30 respectively. Fig. 3 (a): Real reactive power contours of a 3-phase line with EB1 = 0.94, E2 = 0.95 and EB3 = 1.0 p.u
4.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME Fig.3 (b): Real reactive power contour maps of a 4-phase line with EB1 = 0.94, EB2 = 0.95 and EB3 = 1.0 p.u Fig.3 (c): Real reactive power contour maps of a 12-phase line with EB1 = 0.94, EB2 = 0.95 and EB3 = 1.0 p.u It is clear from the above contour maps that the reactive power transfer capacity increases 46 with the increase of number of phases. B. Reactive Power Loss Characteristic The reactive losses (QSL) in an EHV power transmission line are given by = X (2) = Q E I SL B B E Q I X B SL 2 2 0 ( ) If a constant power (QSL= EBIB), is assumed that the rate of change of series reactive power losses with voltage is obtained from (2) as: Q X dQ − SL SL 3 2 0 2( ) B E dV = (3)
5.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME So, the rate of change of reactive power loss with respect to receiving end voltage is inversely proportional of the cube of receiving end voltage. Further an increment in series reactive power losses (dQSL) would be possible with a decline in the transmission voltage in order of EB 47 3. Employing (3) curves of (dQSL /dEB) versus EB (p.u.) are drawn for the sample cases of 3, 4 and 12- phase lines and depicted in fig. 4 for a length of 400 km. dQ SL B dE Fig. 4: Reactive power loss characteristics of three transmission alternatives From the curves in Fig. 4, it is noticed that the series reactive power losses are very small the losses are smaller in multi-phase transmission lines than that in its three-phase counterpart. This implies that the voltage stability limit of multi-phase transmission systems is be increased, making multi-phase systems more secured from the voltage stability view point. Equation (2) can further be written as E I 1 ) ( = Q E I B B = (4) SIL E X B SL B A 2 2 ( ) / where, SIL is the surge impedance loading and is given by EB 2 /X. Based on (4) the results are shown in the plots of QSL versus SIL vide Fig. 5 for a length of 400 km. Fig. 5: Profile of series reactive power losses (QSL) n verses surge impedance loading (SIL) Also from Fig.5 it is seen that the reactive power losses smaller in multi-phase lines. In view of this, multi-phase systems (employing more phases than three) are more secure from voltage stability view point.
6.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME 48 C. Voltage- Power Characteristics If a power transmission line is assumed to be lossless, then the sending and receiving end voltages can be expressed as follow [17]-[22]: A B C cosq sinq (5) − E E jZ B B = + P JQ B E Equation (5) on simplification becomes ( 2 (sin 2 )) 2 0.5 A A C B q q 2cos B E E Z P E ± − = (6) Where ZC is characteristic impedance and is electrical line length expressed as 0.640 ohms/ km. The expression (6) indicates that if sending end voltage is fixed (EA=1.0 p.u.), the receiving end voltage varies with load power factor and line length. using (6), the PB-EB curves are constructed in Figs. 6(a-c) for three alternative transmission systems i.e. 3, 4 and 12-phases assuming line length 400 Km. These figures represent the plots between receiving end voltage and power under specified operating conditions. It is seen that the maximum receiving end power is found largest for 12-phase power transmission system. So, with increased number of phase, maximum power at the receiving end will be progressively enhanced maintaining the voltage stability at various power factors of the load. The above statement is also true for specified load power factor and varying the length of transmission systems, which is evident from Figs. 7 (a -b). Fig. 6 (a): Receiving end voltage profile for varying power flow at p.f .0.94lag for a 400 km line Fig. 6 (b): Receiving end voltage profile for varying power flow at p.f .u. for a 400 km line
7.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME Fig. 6(c): Receiving end voltage profile for varying power flow at p.f. 0.94 lead for a 400 km line Fig. 7 (a): Relationship between receiving end voltage and power at u.p.f and line length of 200 km Fig.7 (b): Relationship between receiving end voltage and power at u.p.f and line length of 400 km IV. ANALYSES OF REACTIVE POWER REQUIREMENTS Assuming EA leads EB by an angel , EA can be written as – 49 d d d E E (cos j sin A j A = + ) (7)
8.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME Substituting (7) in (5) and equating real and imaginary parts of the resulting equation, the relationship between receiving end reactive power and voltages can be written as 50 d q sin ( cos cos ) E E E B B B q C Q B Z − = (8) Similarly, ( cosd cosq ) / sinq A A B A C Q = −E E − E Z (9) If EA=EB then (cosd cosq ) / sinq 2 B A A C Q = −Q = E − Z (10) For lossless line, cos=1, (10) reduces to (1 cosd ) / sinq 2 Q E Zc B A = − (11) where is the transmission angle, ZC is the characteristic impedance and is electrical line length expressed as 0.0012 rad./ km. Employing (11) the terminal reactive power curves as a function of power transmitted for different line length are constructed in Figs. 8(a-b) Fig. 8 (a): Terminal reactive power as a function of Power transmitted for 200 km lines Fig. 8 (b): Terminal reactive power as a function of power transmitted for 400 km lines.
9.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME Figs. 8 (a-b) represent the curves between per unit reactive power and per unit active power for several lengths of 3- phase, 4-phase and 12-phase transmission systems respectively. From examination of these curves, the following observations and conclusions can be derived. When PB P0 (SIL), there is obviously an excess of line charging found. As a result, QA is found negative and QB is obtained positive. This clearly indicates that the reactive power is being absorbed by the system at both ends. Therefore a reactive inductive) compensation is essential for maintaining the voltage stability. While PB P0, reactive power is being generated at both ends. Obviously lagging power factor operation is inevitable. Hence, capacitive compensation is needed for maintaining the voltage stability of the system. Now from the above comparative analysis of the Fig. 8 it is clearly evident that the reactive power requirement to maintain stable voltage varying load is least for highest multi-phase system (12-phase). As the phase order increases, the requirement of reactive power is reduced gradually for different transmission line lengths. This also implies that the rating of the compensating devices for multiphase system will be lower. A. Optimal Reactive Power at Voltage Stability Limit case. Following [22], for lossless line, the power flow equations may be written as-sin 51 P = A B d (12a) B E E X E Q A B B B = cosd − (12b) X E E X The determinant of the Jacobian of load flow equations in a loss less network is given by [19] 1 2 d EAEB EB EA X [ ] ( 2 cos ) D J = − + (13) with [J ] = 0 at voltage stability limit, the receiving end voltage can be written as 2 cosd A B E = E (14) Using (14) in (12b), the value of reactive power at the limiting stage of voltage stability is given by Q = B cos 2d (15) 2 lim E X where, Qlim represents the limiting value of reactive power transfer in a transmission system and it is critical value for voltage breakdown. Using (15), the plot of Qlim with respect to EB has been illustrated through Fig. 9. This figure (Fig. 9) indicates that the reactive power limit for maintaining the voltage stability at different receiving end voltages for transmission line of length of 400 Km with the range of variation from 1.0 pu. to 0.90 p.u. is further observed that the reactive power limit is gradually reducing as the phase-order is increasing from 3-phase to 12-phase at each and every point of per unit receiving end voltage within the range from 1.0 p.u. to 9.0 p.u. Under these circumstances, with increase of number of phases the rating of the devices required from the point of view of compensation is gradually diminished. This also implies that the even in uncompensated mode, the higher phase order system
10.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME performs well from the voltage stability view point since the requirement of reactive power is gradually reduced. Fig. 9: Reactive power limit profile for various systems to have voltage stability for different receiving end voltages 52 B. Shunt Compensation for Voltage Stability Shunt capacity support at voltage stability limit using properties of voltage dependent load [14] is illustrated by the following equation | | | E || Y | Y − − | | sec 2 | | | | 1 0 T B m B A BA SH Y mP E E = − f (16) where PO is the power at rated voltage EB and m is the load characteristics for the voltage dependant loads. Equation (16) provides a relationship for the minimum of SH at load end for getting a stable voltage state under set of specified operating conditions. Figs. 10 (a) and (b) exhibit the magnitude of the minimum receiving end bus admittance at different per unit voltage for different power factors in case of multi-phase systems. The above cases are shown for m = 0.4 and m =1.0 It is observed that enhancement of shunt capacitive support is required to improve the receiving end voltage magnitude from the point of view of the stability of the system voltage in case of voltage dependent load (i. e. m 1). Also the requirement of shunt capacitive support rating for voltage dependent load is gradually reduced as the phase-order of the system is increased from 3 to 12. Fig.10 (a): Profile of minimum magnitude of load end bus admittance at different voltages with 0.94 p.f. lagging at voltage stable states
11.
International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME Fig.10 (b): profile of minimum magnitude of load end admittance at different voltage with u.p.f. at voltage stable state The same analysis has been carried out for variation of length of transmission line and it has been given in Fig. 11. Figs. 11 (a) and (b) represent the curves - shunt admittance (YSH= =Y'BB) versus length (L) for different power factors (0.94 lagging unity) at m = 0.5 and m=1 It can be seen concluded that with increase of number of phases the value of the shunt capacitive rating is reduced for voltage dependent load at voltage stability limit Fig. 11(a): Profile of load end admittance for varying line length with p.f.0.94 lag at voltage stability limit Fig. 11 (b): Profile of load end admittance for varying line length with u.p.f. at voltage stability limit 53
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International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME 54 VI. CONCLUSION The multi-phase lines (4-phase and 12-phase) show progressively increased power handling capacity, reduced reactive power losses, increased power at the receiving end, reduced reactive power requirement for maintaining stable load voltage, reduced rating of compensating devices, better voltage stability in case of voltage dependent load and increased line loadability in uncompensated as well as compensated condition the phase order is increased the multi-phase lines may be very attractive and beneficial to electric transmission utility. REFERENCES [1] L. O. Barthold and H. C. Barnes, High phase order power transmission, Electra, Vol..24, 1972, pp.-139-153. [2] J.R. Stewart and D.D. Wilson, High phase order transmission—a feasibility analyses part- 1steady state considerations, IEEE Trans. PAS- 97., 1978, pp. 2300-2307. [3] S.N. Tiwari, G.K. Singh and A.S. Bin Saroor, Multi-phase transmission research—a survey, Electr. Power Syst. Res., (24), 1992, pp.207-215. [4] T. L. Landers R.J. Richeda, E. Krizanskas, J.R. Stewart, and R.A. Brown, High phase order economics: constructing a new transmission line, IEEE Trans. PWRD-13, No.4, 1998, pp.1521-1526. [5] I.A. Metawally, Electrostatic and environmental analyses of high phase order transmission lines, Electr. Power Syst. Res. 61(2), 2002, pp. 149-159. [6] R. Billinton, S.O. Fareed and M.F. Firuzabad, Composite systemreliability evaluation incorporating a six-phase transmission line, IEE Proc., Vol. 150, No.4, 2003, pp. 413-419. [7] H. Elrefale, Modeling arching faults of six-phase transmission lines, IEE Conf., 2004, pp. 48-51. [8] M.W. Mustafa, M.R. Ahmed and H. Shareef, Fault analysis on double three-phase to six-phase converted transmission line, IEEE Power Engg. Conference, IPBC, 2005, pp. 1-5. [9] Zakir Husain, R.K. Singh, and S.N. Tiwari Multi-phase (6-phase 12- phase) power transmission systems with thyristor controlled series capacitor, Proc. Of the 6th WSEAS Int. Conf. On Application of Electrical Engg. (AEE ' 07), 2007, pp. 246-250. [10] F.D. Glaliana and.Jargis, Quantitative analysis by steady state stabilityin power networks, IEEE Trans. On P.A S. Vol. PAS-100, No.1, 1981, pp.318-326. [11] S. Abe, Y. Fukunaga, A. Isono and B. Kondo, Power system voltage stability, IEEE Trans. On P.A. S. Vol. PAS-101, No.10, 1982, pp.3830-3840. [12] Y. Tamura, M. Mori and S.Iwamoto, Relationship between voltage stability and multiple load flow solution in electric power systems, IEEE Trans. On P.A. S. Vol. PAS-102, No, 5, 1983, pp. 1115-1125. [13] C.S. Indulkar and B. Viswanathan, Effect of series compensation on the voltage instability EHV long lines, Elctr. Power Syst. Reas., No.6, 1983, pp.185-191. [14] A. Chakrabarti and A.K. Mukopadhay, Load end real and reactive power operating contour and shunt capacitive support at voltage stability limit of an E.H.V power system, Proc. SICE-IEEE KAAC International conference Japan, 1989, pp.1001-1003. [15] M.R. Aghamohammadi and M. Mohammadian, Sensivity characteristic of neural network as a tool for analyzing and improving voltage stability, Proc. IEEE Conf., 2002, pp.1128-1132. [16] H. Sun, X. Zhou and R. Li, Accuracy analysis of static voltage stability indices based on power flow model, Proc. IEEE Conf., 2005, pp1-7. [17] T.J.E. Miller, Reactive power control in electric systems, Ist ed., John Wiley, 1982, pp. 67-82.
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International Journal of
Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 10, October (2014), pp. 43-55 © IAEME [18] P. Kundur, Power system stability and control, Ist ed., McGra-Hill, New York, 1993, 55 pp. 216-225. [19] A. Chakrabarti, D.P. Kothri and A.K. Mukhopadhyay, Performance, operation and control of E.H.V. Power Transmission Systems, Ist ed., Wheeler, 1995. pp. 51-160. [20] R.D. Dunlop, R.Gautam and P.P. Machenko, Analytical development of loadability characteristics for EHV and UHV transmission lines, IEEE Trans.Vol. PAS-98, 1979, pp. 606-617. [21] R. Gautam, Application of line loadability concepts to operating studies, IEEE Trans. Vol. PWRS-3, No.4, 1988, pp. 1426-1433. [21] R. Gautam, Application of line loadability concepts to operating studies, IEEE Trans. Vol. PWRS-3, No.4, 1988, pp. 1426-1433. [22] Zakir Husain, Ravindra Kumar Singh and Shri Niwas Tiwari, multiphase (6-phase 12-phase) Transmission Lines performance characteristics IJMACS Trans, vol.1, 2000. [23] D. Pattanayaka, M. Basub and R. N. Chakrabartic, “Multi-Objective Differential Evolution for Optimal Power Flow”, International Journal of Electrical Engineering Technology (IJEET), Volume 3, Issue 1, 2012, pp. 31 - 43, ISSN Print : 0976-6545, ISSN Online: 0976-6553. [24] Suresh J. Thanekar, Waman Z. Gandhare and Anil P. Vaidya, “Voltage Stability Assessment Of A Transmission System -A Review”, International Journal of Electrical Engineering Technology (IJEET), Volume 3, Issue 2, 2012, pp. 182 - 191, ISSN Print: 0976-6545, ISSN Online: 0976-6553.
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