国际大电网输电线路谐波研究-

1、 Appendix A Reference node Reference Cable Figure 13 - Single-line diagram of the 2030 Western Denmark transmission grid. Bold: 400KV; Dashed: 150kV. Blue: Cable-line used in chapters one to three. Red: Cable modelled by means of FD-models in chapter four. Note: Due to differences between the Englis

2、h and Danish names of some cities, the STSV-LEM link is named STS-LKR in the map 11 Appendix B The shunt admittance matrix is equal for both bonding configurations, but the series impedance matrix presents some differences. By applying the method explained in 1, (1 and (2 for the positivesequence se

3、ries impedance of the conductors are obtained. Where ZCC is the core self-impedance with earth return, ZCSi is mutual impedance between core and screen with earth return, ZSS is the screen selfimpedance with earth return, Zboth is the series impedance of a cable bonded in both-ends and Zcross the se

4、ries impedance of a cross-bond cable. Z + both = Z CC - Z CS 2 ( Z - ZCS 2 ) + CS 1 Z CS 2 - Z SS 2 (1 (2 + Z cross = Z CC - Z CS 2 The resonance points have higher magnitudes and lower frequencies for the cross-bond cable than for the both-end bonded cable. As the differences in the resonances are

5、noticeable for the first resonance point, the nominal pi model instead of the equivalent pi model can be used, which results in a simple mathematical analysis. The line impedance for the nominal pi model is given by (3. (1 - w LC ) + j (w RL ) Z= ( -w C R ) + j ( 2wC - w C L ) 2 2 2 3 2 (3 The shunt

6、 admittance is equal for both bonding types and the differences in the impedance are a function of L and R. Resonance Frequency The resonance frequency is given by (4, which is obtained by developing (3. L is the imaginary part of the series impedance (1-(2. Consequently, the imaginary part of Z+cro

7、ss>Z+both. Subsequently, the imaginary part of the last element of (1 should be negative, i.e. (5. w2 = 2 LC (4 (5 æ ( Z CS 1 - Z CS 2 )2 ö ÷<0 imag ç ç Z CS 2 - Z SS ÷ è ø Both the real and imaginary parts of ZSS are always larger than the equivalents i

8、n ZCS2. Thus, the denominator of (5 has always a negative real and imaginary part (6. Z CS 2 - Z SS = -a - jb The development of the numerator of (5 results in (7. (6 ( ZCS1 - ZCS 2 ) 2 = ( ( c + jd ) - ( e + jf ) ) = ( c 2 - d 2 + e 2 - f 2 - 2ce + 2df ) + j ( 2cd + 2ef - 2cf - 2de ) (7 2 The magne

9、tic field is stronger between the core and screen of the same cable than between the cores or core-screen of two different cables. Thus, d>f while ce, and so (7 can be simplified to (8. 12 ( ZCS1 - ZCS 2 ) 2 = ( -d 2 - f 2 + 2df ) + j 0 Û ( Z CS 1 - Z CS 2 ) = - d 2 - ( d - g ) + 2d ( d - g

10、) 2 2 2 2 2 2 2 2 2 ( ) Û ( Z CS 1 - Z CS 2 ) = -d - d - g + 2dg + 2d - 2dg Û ( Z CS 1 - Z CS 2 ) = - g (8 It is concluded that the numerator of (5 has only a negative real part. Therefore, (5 can be written as (9. ( ZCS1 - ZCS 2 ) Z CS 2 - Z SS 2 = -g 2 = - g 2 × ( -a '+ jb '

11、) - a - jb 2 ( Z - ZCS 2 ) Û CS 1 Z CS 2 - Z SS (9 = (a ' g 2 ) + j ( -b ' g ) 2 The imaginary part of (5 is always negative and the resonance frequency of a cross-bond cable is always lower than the resonance frequency if bonded at both-ends. Magnitude Parallel resonance From (3 the ma

12、gnitude is given by Z = (1 - w LC ) + jw RC Û 2 -w RC 2 2 Z = (1 - w LC ) + 2 -w RC 2 2 jw RC L Û Z = +j 2 2 -w RC 2 RC 2 3 L C2 2 LC (10 Û Z = L2 L3 æLö 1 æLö 1 + Û Z = ç ÷ +ç ÷ 2 2 3 2 4C R 2C è C ø 4R è C ø 2 The two

13、variables that depend on the bonding are R and L, which are, respectively, the real and imaginary parts of the series impedance matrix (to be precise, the imaginary part is XL, but for this analysis, that is not very relevant. From the analysis of the resonance frequency and (1, (2 and (9 it is know

14、n that the both-end bonded cable has a higher resistance and a lower inductance. Doing the substitutions in (10, it is concluded that the magnitude of the parallel resonance points is lower in the both-end bonded cable. Series resonance For a series resonance, the impedance magnitude is given by (11

15、. The value of L is lower for a bothend bonded cable, resulting in lower magnitude at the series resonance points for this type of bonding. Z= j (w RL ) -w C R 2 2 Û Z = L L LC Û Z = 2 wC 2C 2 (11 13 BIBLIOGRAPHY 1 2 3 4 5 6 7 8 9 F. Faria da Silva, “Analysis and simulation of electromagne

16、tic transients in HVAC cable transmission grids”, Ph.D. Dissertation, Dept. Energy Technology, Univ. Aalborg, 2011 CIGRE WG B1.19, “General Guidelines for the Integration of a New Underground Cable System in the Network”, CIGRE Technical Brochure 250, 2004 CIGRE WG B1.07, “Statistics of AC Undergrou

17、nd Cables in Power Networks”, CIGRE Technical Brochure 338, 2007 Mohamed Abdel-Rahman, "Frequency Dependent Hybrid Equivalents of Large Networks", PhD Thesis, University of Toronto, 2001 PSCAD Application Notes, "Converting a Solved PSS/E Case to PSCAD for Transient Simulations",

18、 2006 IEEE Guide for the Application of Sheath-Bonding Methods for Single-Conductor Cables and Calculation of Induced Voltages and Currents in Cable Sheaths, IEEE Std. 575-1988 IEC 62067, "Power cables with extruded insulation and their accessories for rated voltages above 30 kV (Um=36kV up to 150 kV (Um=170 kV - Test methods and requirements", Edition 3.0, 2004 IEC 60840, " Power cables with extruded insulation and their accessories for rated voltages above