Grid impact analysis of a HTSC cable by using an

enhanced conventional simulator

Gerard Del-Rosario-Calaf1, Andreas Sumper1,3, Xavier Granados2

and Antoni Sudria-Andreu1,3

1 CITCEA-UPC Escola Universitaria d’Enginyeria Tecnica Industrial de Barcelona,Universitat Politecnica de Catalunya, C. Comte d’Urgell 187, 08036 Barcelona, Spain2 ICMAB-CSIC, Campus UAB, 08193 Cerdanyola del Valles, Spain3 Catalonia Institute for Energy Research (IREC)

E-mail: sumper@citcea.upc.edu

Abstract. Conventional simulators for power system studies do not include the newsuperconducting (SC) elements in order to perform analysis of their behaviour on the grid,however these simulators allow users to include external functions specifically designed. In thiscase, a specific library with the corresponding physical model of Very Low Impedance SC cableshas been designed and included. This article reports on the developed algorithm and the resultsobtained by applying it to standard grids including SC cable.

1. IntroductionHigh temperature superconducting cables have been arisen as a solution for saturatedunderground urban areas and for retrofits, wherever space is a constraint and power ratingmust be significantly increased to satisfy demand. Several pilot projects have been executedworldwide since 1997, with some of them including operation of SC cables on the grid [1]. Inthat sense, grid operators must include this new type of power transmission cable in their regulargrid studies, such as the load flow study. In this type of study, modeling of SC cables understeady state conditions is required. Standard power system simulation programs include theequivalent pi model of transmission line to represent cable parameter like resistive, inductiveand capacitive losses [2]. However, AC losses associated with current transmission through SCcables have different behaviour than resistive losses in conventional cables, as reported by [3]or [4]. Despite this, in load flow studies, representation of AC losses is usually simplified at aconstant equivalent resistance value in the pi model [5]. This paper proposes a new algorithmto simulate AC losses in SC cables pi model to be used in load flow studies using conventionalpower system simulation programs. This work includes algorithm design and its implementationwith Python programming language, and an example of SC cable integration on the grid usingPSS/E program.

2. Cable ModelingThe electric parameter model that is established for the cable superconductor corresponds tothe equivalent pi model of transmission line depicted in 1, usually used in studies of powersystems. In conventional lines, line resistance Rt represents Joule losses and the reactance

Xt and susceptance Bt, that represent magnetic and electric field, respectively. In Very LowImpedance SC cables, Rt will represent AC losses instead of joule effect losses, due to the differentbehaviour of this type of cables compared to conventional power lines. However, Xt and Bt havethe same physical origin in SC cables as in conventional cables.

ofI foIrmsItR tX

2tB

2tB

BI1 BI 2

oV fV

Figure 1. Equivalent pi model of a transmission line. Rt, Xt and Bt correspond to equivalentresistance, reactance and susceptance of the transmission line, respectively.

Xt and Bt of Very Low Impedance SC cables are calculated as

Xt = (ω · L) · l (1)Bt = (ω · C) · l (2)

where ω is the base angular frequency of the grid, L is the equivalent inductance per unitlength, l is the cable length, and C is the equivalent capacitance per unit length. Both L and Chave known expressions reported in literature [5] by

L =µ0

2πln(rsr2

)(3)

C =2π ε0 εrln(

rsr2

) (4)

where µ0 is the magnetic constant, rs is the radius of the SC shield, r2 is the outer radius ofone SC phase, ε0 is the electric constant and εr is the relative permittivity of the dielectric.

On the other hand, cable AC losses, PAC , are expressed as a function of RMS current, Irms,for both states, i.e. hysteresis losses and hysteresis losses combined with flux-flow regime losses

PAC = K1 Iq1rms (Irms < Inom) (5)

PAC = K2 Iq2rms (Irms > Inom) (6)

where K1, K2, q1 and q2 are empirical parameters, Irms is RMS current through the cablebranch between original bus and end bus and Inom is the SC cable nominal current.

In this work, the expressions for AC losses are used for the development of the expression tocalculate the value of the resistance Rt. The conversion of the AC losses value to the resistancevalue is carried out with an analogous expression of Joule’s First Law for conventional conductors

Rt =PAC

I2rms

(7)

leading to

Rt =

K1 I

q1−2rms (Irms < Inom)

K2 Iq2−2rms (Irms > Inom)

(8)

3. AC losses calculation algorithmAs shown in (5), (6) and (8), it is necessary to know Irms value to calculate AC losses or itsequivalent Rt. On the other hand, pi model is a suitable model for load flow calculations, whichallow to know relevant information about power systems operation, for instance, AC currentinjected from one bus to another bus. In this work, an iterative algorithm based on utilizationof expression (8) and load flow resolutions to approach Rt real value is proposed. This algorithmis depicted in Fig. 2.

First of all, an initial Rt value is estimated and it is introduced in the SC cable pi model. Rt

value may be estimated to a reasonable value. Afterwards, a load flow calculation is executed,and an initial Irms value is obtained for the SC cable. Next, an alternative value for Rt iscalculated by applying the Irms value in (8). Finally, the absolute value of the discrepancybetween both Rt values is compared with an acceptable absolute error, named epsilon. Fromthis point, a bifurcation point occurs. If the discrepancy between both Rt values does not exceedepsilon’s value, the initial Rt estimation is considered to be good enough and the algorithmfinishes. On the contrary, if this discrepancy does exceed epsilon’s value, then the initial Rt

estimation is considered not to be good enough, and an iteration loop starts. Each iteration isexecuted as follows. Every Rt value that is calculated in the previous iteration is introducedin the SC cable pi model in order to execute a new load flow calculation. Then the Irms valueobtained from load flow calculation is introduced in (8) in order to obtain a new value for Rt.Finally, discrepancy between both Rt values is evaluated again.

4. Integration of the Cable in the Power System Simulation ProgramThe proposed methodology for the integration of the SC cable in the power system simulationprogram is structured in two parts. First, a selected grid is modeled, and second, AC lossescalculation algorithm is executed.

The grid modeling is a process that can be divided in three main steps. First of all,introduction of model parameters of all grid elements is performed. SC cable pi model is alsoincluded in the grid modeling, except the resistance value, representing AC losses, which is anunknown parameter. Secondly, the bus classification and variable initialization is executed. Inthe last step, a load flow resolution algorithm is executed, such as Newton-Raphson or decoupledNewton-Raphson methods.

At the end of the methodology’s first part, the grid is completely modeled in steady stateoperation except for SC cable AC losses. In the second part, AC losses calculation algorithm isexecuted, as explained in section 3.

PSS/E program, version 31.0.0, is used for the power system simulation Program that hasbeen used is . Phyton programming language has been used for the algorithm implementation.

This methodology has been verified with a particular example in PSS/E. The verificationconsists in the comparison between AC losses measured in a real cable and AC losses obtainedwith the algorithm under different Irms values.

The test grid is composed by one generator, one load an one SC cable, depicted in Fig.3. Bus number 1 is slack type bus at 13,8 kV, 0 degrees, and bus number 2 is PQ type bus.The generator consumes zero apparent power and the load generates zero apparent power andconsumes inductive power with power factor equal to 0,8. The grid base frequency is set to 60Hz.

- Estimated resistance value

- Cable lengthRm:= estimated resistance value

Substitution of current Rm value in model

- Original bus

- Final bus

- Cable identification

Power Flow resolution- Resolution algorithm

Calculation of current Irms value

- Original bus

- Final bus

- Cable identification

Calculation of current resistance value

- Cable nominal current

- k1 and q1 parametres

- k2 and q2 parametres

- Cable length

- Grid base frequency

Rm+1:= current resistance value

abs(Rm+1 - Rm) > epsilon ? END

NO

Substitution of current Rm value in model

- Original bus

- Final bus

- Cable identification

Power Flow resolution - Resolution algorithm

Calculation of current Irms value- Original bus

- Final bus

- Cable identification

Calculation of current resistance value

- Cable nominal current

- k1 and q1 parametres

- k2 and q2 parametres

- Cable length

- Grid base frequency

YES

Rm:= Rm+1

Rm+1:= current resistance value

BEGIN

Figure 2. AC losses calculation algorithm flux diagram

Figure 3. Grid diagram for methodology’s verification.

Table 1. Cable specifications. Data from [3], voltage modified to 13, 8 kV.

Description Value

Nominal current 1250 ANominal tension 13,8 kVCable configuration Three phases in one cryostat.Dielectric type Cold dielectric.Dielectric material PPLP (4,5 mm).

On the other hand, SC power line between buses 1 and 2 consists of a one km length three-phase cable and the majority of its specifications are obtained from [3], except for the nominalvoltage, that is set to 13,8 kV instead of 22,9 kV. SC cable parameters are shown in Table 1.

The initial resistance value is estimated at 1e-6 pu (1,904e-6 Ω) and the epsilon value is set to1e-6 Ω. Newton-Raphson is the Power Flow resolution method selected for the methodology’svalidation.

The results are shown in Table 2 and Fig. 4. In all cases, algorithm convergence was reachedafter three iterations.

5. Application ExampleThe algorithm presented in this article is intended to be a tool suitable in studies involvingintegration of SC power cables in real power systems, which are more complex than the gridpresented in the methodology’s validation. An example of application of this algorithm in arealistic grid model will be explained in this section.

The test grid system is provided by PSS/E [6], depicted in Fig. 5. In this test system, thegenerator called Urbgen- bus number 206, is moved to another location and is re-connected tothe grid through a new SC power line. The initial and the later cases are shown in Fig. 6. Theinitial case is drawn in dotted line. A new bus is created in the grid in order to represent thenew connection point between one SC line end and the substation. The new SC line is composedof five three-phase cables that have the parameters shown in Table 3.

The objective of this example is to calculate the line length corresponding with a maximumvoltage drop set at 5%. Results for different voltage drops are shown in Table 4. The line with5% voltage drop is 27 km.

Table 2. Results for the methodology’s validation.

S load P load Q load R I rms AC losses(MVA) (MW) (Mvar) (Ω/km) (A) (W/m/phase)

36 28,8 21,6 0,00367 1510,2 8,37334 27,2 20,4 0,00277 1426,0 5,63132 25,6 19,2 0,00205 1341,6 3,69730 24 18 0,00149 1257,5 2,36428 22,4 16,8 0,00106 1173,4 1,46427,22 21,78 16,33 0,00093 1140,9 1,20527 21,6 16,2 0,00092 1131,4 1,17626 20,8 15,6 0,00091 1089,5 1,08424 19,2 14,4 0,00090 1005,4 0,91020 16 12 0,00087 837,5 0,61216 12,8 9,6 0,00084 669,7 0,37712 9,6 7,2 0,00080 502,0 0,202

103

10−2

10−1

100

101

RMS current [A]

AC

Los

ses

[W/m

/pha

se]

Figure 4. AC losses obtained with the algorithm.

Table 3. SC cable parametres.

Parametre Value Units

R 10−3,5555 (Irms)0,1699 500A < Irms < 1138, 9A Ω/km

10−18,041 (Irms)4,9090 1138, 9A < Irms < 1500A

L 0, 056 mH/kmC 441 nF/km

101NUC-A

1

102NUC-B

1.02022.016.5

1

81.2

R

46

5.9

-168

.0

-460

.4

-94.

6

465.

9

-168

.0

-460

.4

-94.

6

201HYDRO

1.040520.06.2

1

740.

0-7

40.0

1.009504.4-1.3

3004WEST

154DOWNTN

1

600.

0

450.

0

2

350.

025

1.6

100.

4

-247

.9

209.

7

80.4

-206

.6

14.1

1

300.

0

150.

0

123.

2

52.7

205SUB230

1 354.

9

1

75.0

-88.4

69.3

64.0

555.

8

12.9

-549

.8

-148

.0

592.

4

26.1

-83.

3

-29.

7

83.8

-83.

3

-29.

7

1.02418.4-3.0

1

3001MINE

3002E. MINE

3003S. MINE

202.

5

84.8

-202

.5

-81.

2

11.6

3005WEST

0.995228.8-5.2

1

100.

0

50.0

40.6

-100

.6

-43.

4

101.

3

40.6

-100

.6

-43.

4

-78.

4

81.2

R

- 472

. 8

600.

0

600.

0H

-1

34.5

-251

.5

0.993228.4-3.2

-590

.7

1.016508.2-3.4

100.

0

101.

3

78.6

81.2

138.

2

-137

.7

-114

.6

152MID500

81.2

3008CATDOG

1.023235.4-2.3

56.0

-55.

8

1

600.

0

3011MINE_G

1

258.

7

104.

0R

1

100.

0

80.0

H

17.8

R

211HYDRO_G

1.04020.812.9

53.0

17.8

-258

.5

-96.

9

258.

7

104.

0

56.0

12.0

-56.

0-1

1.6

133.

8

-193

.2

-125

.1

-100

.010

0.0

80.0

54.0

135.

9

-54.

4

-78.

6

-138

.3

1.012505.910.9

203EAST230

0.939216.0-9.9

-797

.5

200.

0

250.

5

800.

0

0.994228.6-3.8

-66.

6

1.030236.9-1.4

0.959220.5-9.0

9.1

-69.0

400.

0

0.967222.3-6.9

-19.

2

193.

4

151NUCPANT

750.

0

1200

.0

1.02214.1-4.1

3018CATDOG_G

3006UPTOWN -1

4.1

1.028514.0-1.8

200.

0

78.7

-66.

1

1.02022.016.5

-6.8

-748

.4

1.017508.5-1.1

-6.8

-264

.529

5.8

-354

.2

206URBGEN

700.

0

-42.

6

600.

0

0.949218.3-9.2

26.1

83.8

-208

.327

6.5

-122

.4

-53.

9-75.

875

0.0

-264.8

-128

.5

800.

0

31.8

42.7

AREA 1 (FLAPCO) AREA 2 (LIGHTCO)AREA 5 (WORLD)

564.8

130.9 MW-538.3 Mvar

358.7 MW184.0 Mvar

1000.0 MW800.0 Mvar

Area 1 to 2 Interchange

Area 5 Generation

Bus 154 Load

PSS(TM)E PROGRAM APPLICATION GUIDE EXAMPLEBASE CASE INCLUDING SEQUENCE DATA

THU, AUG 21 2008 13:58SAVNW

<=18.000 <=21.600 <=500.000

90.0%RATEA 0.950UV

<=20.000 <=230.000KV: <=13.800 >500.000

1.050OV

Bus - VOLTAGE (KV/PU)/ANGLEBranch - MW/MVAREquipment - MW/MVAR

153MID230

750.

0

-748

.4

750.

0

191.

2

-561

.3

202EAST500

-16.3

1.04014.40.0

1 0.

0

614.

4

1

0.0

-324

.5

-597

.7

1

0.0

-46.

7

1

0.0

-270

.2

603.

2

67.3

-590

.7

-148

.2

236.

8

98.8

-34.

8

-18.

0

1

0.0

-264

.5

Figure 5. PSS/E SAVNW grid test system.

Figure 6. Introduction of a SC power line in SAVNW grid (PSS/E image).

Table 4. Voltage drops between buses 3018 and 1.

length voltage voltage dropbus # 3018 bus # 1

(km) (p.u.) (p.u.) (%)

5 1,0299 1,0208 0,9110 1,0379 1,0199 1,8015 1,0459 1,0191 2,6820 1,0537 1,0183 3,5425 1,0615 1,0176 4,3930 1,0692 1,0169 5,2330,5 1,0700 1,0168 5,32

6. ConclusionsIn this work, development of an new algorithm to calculate AC losses of SC cables has beensuccessfully executed. A suitable electrical equivalence between AC losses and a resistiveparameter has been proposed in order to enable the utilization of the SC cable model inconventional power system simulation programs. The algorithm has been implemented withPython programming language and the SC cable model has been used in PSS/E. Both algorithmand model have been validated in a particular case with real data obtaining successful results.An application example of the connection of a generation unit to a standard PSS/E grid througha SC power line has also been executed. The algorithm and its corresponding physical modelhere proposed are restricted to AC steady state operation conditions. Dynamic characterizationof SC cables could be considered in future works.

AcknowledgmentsWe would like to acknowledge encouragement from colleagues from CITCEA-UPC, ICMAB-CSIC and Catalonia Institute for Energy Research (IREC). ENDESA-NOVARE project”Supercable”, MICINN MAT2008-01022 , ”Nanoselect” Consolider, and Xermae, contributionsare also recognized.

References[1] Prusseit W 2008 IEEE/CSC & ESAS European Superconductivity News Forum 4[2] Exposito A G 2002 Analisis y operacion de sistemas de energıa electrica. (Mc Graw Hill)[3] Sohn S H, Hwang S, Lim J, Yim S, Hyun O, Kim H, Yatsuka K, Masuda T, Isojima S, Watanabe M, Ryoo

H, Yang H and Kim D 2007 Physica C: Superconductivity 463-465 1146–1149[4] Wen H M, Lin L Z, Lin Y B, Gao Z, Dai S T and Shu L 2003 Physica C: Superconductivity 386 52–55[5] Howe J, Kehrli B, Schmidt F, Gouge M, Isojima S and Lindsay D 2003 Very low impedance (vli)

superconductor cables: concepts, operational implications and financial benefits. a white paper. Tech.rep. American Superconductor; Nexans Deutschland; Oak Ridge National Laboratory, Sumitomo ElectricIndustries and Ultera

[6] PSS/E Program Manual