Integration of IEC 60287 in Power System Load Flow for ... · B. System Design for Power...

Integration of IEC 60287 in Power System Load

Flow for Variable Frequency and Long Cable

Applications

X. Yuan, H. P. Fleischer, G. Sande, and L. J. Solheim

GE Oil and Gas, Norway, NO1338Norway Email: {xu.yuan, hans-peter.fleischer, gorm.sande, lars.joar.solheim}@ge.com

Abstract—AC resistance, usually paid less attention to than

inductance and capacitance during power system design

work, may cause significant deviation to true result if not

well controlled during load flow design for variable

frequency and long cable applications. In this paper, a load

flow scheme integrating cable design with power system

design is proposed, benefiting from IEC 60287. With thermal

consideration based on IEC 60287, AC resistances at load

current taking into account the longitudinal distribution of

current are iterated in a power load flow. Case results

demonstrated that the correct consideration of AC resistance

is critical to the derivation of true result. The proposed load

flow scheme naturally bridges the gap between cable

engineering and power system engineering and reduces the

uncertainty in system design work for variable frequency

and long cable applications.

Index Terms—load flow, variable frequency, submarine

cables, subsea power, wind power, mat power, IEC 60287

I. INTRODUCTION

Nowadays, more and more offshore wind farms are

being or going to be connected to grid with a distance of

over 150km. With today‟s manufacturing capability of

high voltage XLPE insulated three-core submarine cable

and the robustness of AC system, AC transmission

solution with long HVAC cable is still the first choice to

be evaluated, with an emphasis on the investment cost as

well as cost of transmission losses. Small difference in the

transmission losses over long cables could lead to large

differences in energy output over a 20 year life time [1],

which might further lead to a wrong picture when

comparing the different transmission alternatives.

Another emerging demand for long power cables comes

from the development of subsea oil pumping and gas

compression, which requires MW level of power for each

subsea consumer with step-out distance ranging from tens

of kilometers to a couple of hundred kilometers. In

addition to long submarine cables, the application usually

requires variable speed drives (VSDs) located on the

offshore production platform which introduces variable

frequency operation (up to 200Hz for high power subsea

compressor motors) over long cables [4], [5].

Manuscript received September 4, 2012; revised December 24, 2012.

Due to the dominantly capacitive characteristic of long

submarine cables, coupled with varying frequency, careful

consideration of current distribution in the cable and

reactive compensation strategy becomes vital when

designing the system in a steady state load flow domain.

The fact that cable engineers and electrical system

engineers usually work as two separate disciplines also

calls for an integrated methodology when performing a

power system load flow analysis.

In this paper, a load flow scheme directly integrating

cable design based on IEC 60287 is proposed. Its

implementation with power system load flow is based on

Matpower Version 4 [3]. Results show that a proper

consideration of cable design, current distribution along

cable and reactive compensation strategy altogether has

vital contribution to power system load flow design for

variable frequency and long cable applications.

II. PROBLEM FORMULATION

The motivation of the proposed load flow scheme

comes from the previously mentioned industrial

applications and more specifically described as the

following 3 main areas:

A. Loss Evaluation for Offshore Wind Farms

Offshore wind power is connected to onshore grid by

submarine cables and this distance can be up to 150km or

more, shown in.

GridOffshore

Substation

Offshore wind

Long submarine cable

Figure 1. Offshore wind grid connection via long AC cable.

Reactive power compensation is used either onshore or

at both ends of the cable. Due to the intermittent intrinsic

of wind power generation, remarkable variations of

current present in the compensated long cable. H.

Brakelmann in [1] proposed to derive the transmission

losses of the power cable taking into account the

longitudinal distributions of current and temperature:

6

International Journal of Electrical Energy, Vol.1, No.1, March 2013

©2013 Engineering and Technology Publishingdoi: 10.12720/ijoee.1.1.6-11

𝑷𝑳𝒐𝒔𝒔 =𝑷𝑰𝒎𝒂𝒙

𝒍𝟎∙

𝑰𝟐(𝒙)

𝑰𝒏𝟐(𝒙)

∙ 𝒗𝜽(𝒙) ∙ 𝒅𝒙𝒍𝟎𝒙=𝟎

(1)

Where 𝐼𝑛 is the current rating of the cable and 𝑃𝐼𝑚𝑎𝑥 is

the nominal ohmic losses of the cable for 𝐼𝑛 . 𝑣𝜃 is the

calculated correction factor considering an ambient

temperature for a specific 𝐼. The above calculation assumes that the actual current

flowing along the cable has been determined, in other

words, the transmission system has been designed.

However, ideally as early as when designing the

transmission system, the variation of currents – in fact the

variations of resistances due to variations of current, shall

already be considered in the load flow design. And by

doing so, the calculation of power losses will then be

straightforward – difference in MW between cable input

and output.

This idea indicates the need of a load flow scheme that

integrates the variations of resistances along the cable due

to temperature dependence so that the loss evaluation can

be facilitated as a standard direct output from the load flow

design.

B. System Design for Power Distribution with Long

Cables

More and more offshore platforms and subsea stations

are requiring power (up to 50MW) from land remotely via

long submarine power cables (over 100km) for the

Oil&Gas industry [4]. Due to tough environment and

limited space, reactive compensation is preferred to be

done at one end onshore. Such a system is shown in Fig. 2.

Onshore/Platform Subsea transformer

Subsea Switchgear

Long submarine cable

M

M

M

M

Subsea VSD

STATCOM

Figure 2. Power distribution with long cable.

The design of such a system requires close look at the

voltage and current along the cable as well as loss

evaluations for different AC solutions and DC solutions.

C. System Design for VSD Driven Motor with Long

Cables

Applications of VSDs on large induction motors are not

new in the power industry. However, most applications for

subsea electrification involve a step-out distance,

requiring long cables between the motor and VSD[8].

Such a system is shown in Fig. 3.

Subsea Motor

Variable frequency over long cable

Topside VSD

M

Figure 3. VSD driven large motor with long cable step-out.

This long cable turns a direct VSD driven system to a

„variable frequency transmission system‟ due to the fact

that power system load flow is required to determine cable

size, transmission voltage and power losses. Furthermore,

variable frequency adds to the dimension of the design

which affects the voltage profile on the long cable.

Coupled with higher frequency (than 50Hz) output from

the VSD (up to 200Hz) and ambient situation of submarine

cables, the AC resistance of the cable becomes puzzling

yet vital to the correct derivation of system load flow

results.

III. METHODOLOGY

As stated, a load flow scheme directly integrating cable

design based on IEC 60287 is proposed. Previously, work

on estimating cable ampacity had been discussed a lot

however without looking at a power system impact [9],

[10]. This scheme is to bring power system design and

submarine cable design together. Power system load flow

highly depends on the RLC values of the long cable

presenting in the system. Power loss in particular is

relevant to the resistance value. While these values are

indeed available from cable manufacturer‟sdatasheet, only

DC resistances are usually provided. The actual operating

temperature of the cable is also not known beforehand

since it depends on the power losses (currents) and the

thermal conditions of submarine cables. And the currents

along the cable can vary remarkably. Therefore

traditionally during power system load flow, it is not

straight forward to take all these factors into consideration.

Newton Raphson Load Flow iterations

AC ResistancesL, C

Proximity Effect

Skin Effect

Define Power System Topology

Cable Geometric Design

Loss Factors

Define Power System Parameters

Select Cable

Cable Loading OK?

Vo

ltag

e &

C

urre

nt

No

Voltage Profile OK?

Ye

s

No

Environmental Conditions

Current

Temperature

END

Cable Ampacity

Figure 4. Flow chart of the proposed load flow scheme.

The actual AC resistances at steady state along the cable

vary and shall be calculated with skin effect, proximity

effect and the actual conductor temperatures which are not

known without thermal calculation. The proposed load

flow scheme incorporates cable geometrics and adds

additional iterations to the load flow core by updating the

7


©2013 Engineering and Technology Publishing

AC resistance according to the longitudinal currents in the

cable. It has to run outside the Newton Raphson iteration

since it also affects reactive power compensation for the

cable. The thermal calculation is performed based on IEC

60287 in which an analytical method of calculating

thermal condition, skin effect and proximity effect is

presented [11], [12].

A flow chart of the proposed load flow scheme is

presented in Fig. 4.

The initiation of load flow is achieved by using either

the maximum AC resistance at 90°C which is derived

from a cable ampacity calculation, or the AC resistance at

base load current derived from thermal calculation. The

base load current can be derived simply by the load

apparent power (MVA) and the defined transmission

voltage (kV). The additional iterations update the AC

resistances according to the line currents derived from the

load flow. This outer loop of iterations will converge

within 3 rounds.

For the 3 main industrial applications mentioned in this

paper, most of the cables used are three-core submarine

cable with separated sheath and common armouring.

Therefore for this work, the „SL‟ type in IEC 60287 is the

most relevant. However, the proposed load flow scheme

can adapt to any type of cable geometry design and

formation.

IV. IMPLEMENTATION

The implementation of the proposed load flow scheme

is in Matlab with Matpower Version 4 modified as its load

flow core. The major building blocks for implementing the

proposed load flow scheme are discussed below.

A. Matpower

Matpower is a Matlab-based tool widely used in

research and education for AC, DC and optimal power

flow simulations. It consists of a set of M-files designed to

give the best performance while keeping the code simple

to customize [3]. Newton-Raphson, Fast-decoupled and

Gause-seidel method are optional for AC power flow

analysis which are not discussed in this paper and can be

referred to [3].

B. Cable Modelling

Long cables are modeled with „Pi‟ sections with lump

parameter for every kilometer. This is more than sufficient

for power flow analysis with frequency up to 200Hz. And

in this way the longitudinal current distribution is directly

considered. Cable capacitances are modeled as shunt

susceptances 𝐵sh . Each connecting point is treated as one

„PQ‟ bus. The derivation of cable inductance and

capacitance comes from cable geometry and its

installation method pre-calculated in a cable database.

This facilitates the integration of cable design into power

system design. It is also noted that this cable geometry

shall involve detailed design information of cables, i.e. the

thicknesses and material properties of all layers. AC

resistances, usually paid with less attention by power

system engineers, are iteratedby thermal calculation based

on IEC 60287.

C. Reactive Compensation

Active reactive compensations (FACTS devices) are

frequently applied in the 3 industrial applications

mentioned. In this work, steady state STATCOM is

modeled with additional PV bus connected to its

controlling bus via a coupling reactance. Due to the fact

that industrial power supply often utilizes OLTC for

voltage control for remote buses, reactive control mode is

used for STATCOM in this work to control the power

factor at grid connection point. Therefore, the generating

voltage at the additional bus is tuned to give a unity power

factor at grid connection point with its principle given by

where the angular difference is neglected according to the

steady state model given in Fig. 5.

𝑸 =𝑼(𝑼−𝑬)

𝑿𝑺𝑻 (2)

VSC

Controlled Bus

Additional Bus

U,Ɵ

E,Ɵ’

XST

Figure 5. Steady state modeling of STATCOM.

Correct implementation of reactive compensation is

vital in such applications since it directly affects the

current drawn in the cable.

D. IEC 60287

IEC 60287 is applicable to the conditions of steady state

operation of cables at all alternating voltages buried

directly in the ground, in ducts troughs or in steel pipes,

both with and without partial drying-out of soil, as well as

cables in air [11] and [12]. It provides analytical formulae

for current rating and losses leaving certain parameters

open such as material properties, ambient conditions and

burying depth. Skin effect, proximity effect, screen losses

and armouring losses are considered for different cable

formations. For submarine power cables, the most

important environmental inputs to the AC resistance value

are the thermal resistivity of soil, the buried depth as well

as the seabed temperature.

V. CASE RESULTS

Three different case results are derived to demonstrate

the influence from AC resistances for the 3 applications

mentioned. Each calculation is performed with three

different types of AC resistances:

𝑹𝟏 , which represents a constant „guessed‟ value

without considering cable condition and

longitudinal current distribution. In fact, a

maximum AC resistance is used.

𝑹𝟐, which represents a constant value considering

cable thermal condition based on IEC 60287. In fact,

8



an AC resistance calculated from base load current

is used.

𝑹𝟑 , which represents „true‟ AC resistances

considering both cable thermal condition and

longitudinal current based on IEC 60287.

A. Case Result 1 – Power Distribution with Long

Cables

The first case result is derived from the proposed load

flow scheme for the system given in Fig. 2.

TABLE I. CASE RESULTS 1 – POWER DISTRIBUTION WITH LONG

CABLES

150km, 50Hz, 20MW, 5Mvar (full load)

72.5kV rated, 3×240mm2 cable

66kV operation, OLTC 1.04 to control load end voltage

30MVA onshore transformer, 30MVA subsea transformer

AC

resista

nce

Cable end

voltage

(kV)

STATCO

M (Mvar)

STATCO

M voltage

Cable

loss

(MW)

R1 67.40 26.87 -0.0897 p.u. 2.221

R2 68.54 27.61 -0.0898 p.u. 1.753

R3 68.49 27.55 -0.0898 p.u. 1.787

According to the results summarized in Table I, the

differences in reactive compensation caused by different

AC resistances are minor. However, differences in voltage

and cable loss are not negligible. Considering 𝑅3as „true‟

value, the cable end voltage has nearly 1kV deviation with

approximately 20% difference in resistance (𝑅1).

Figure 6. AC resistances along the cable (R1, R2 and R3) – case result 1.

Figure 7. Voltage along the cable derived with different R–case result

1.

Cable loss deviates from „true value‟ correspondingly.

𝑅2 generates very close results to 𝑅3 indicating that the

longitudinal current distribution is not important for this

case. This is due to the balanced cable current sized for full

load condition.

Figure 8. Power losses along the cable derived with different R – case

result 1.

According to Fig. 7, the voltage profile over the entire

length of cable based on 𝑅1 deviates significantly from

„true value‟ based on 𝑅3, to an extent that it could result in

redesign. It also demonstrates the need of correct

consideration of resistance s in a controlled manner.

B. Case Result 2–Power Distribution with Long Cables,

Light Load

The second case result is derived in the same way as in

the first case but with half load. Results are summarized in

Table II.

TABLE II. CASE RESULTS 2 – POWER DISTRIBUTION WITH LONG

CABLES WITH LIGHT LOAD

150km, 50Hz, 10MW, 2.5Mvar (half load)

72.5kV rated, 3×240mm2 cable, inner layer

66kV operation, OLTC 0.97 to control load end voltage


AC

resistanc

e

Cable end

voltage

(kV)

STATCO

M (Mvar)

STATCO

M voltage

Cable

loss

(MW

)

R1 66.01 28.42 -0.0953 pu 1.537

R2 66.65 28.77 -0.0953 pu 1.194

R3 66.59 28.73 -0.0953 pu 1.243

As a response to reduced load, OLTC has a low position

(0.97) to control the voltage. According to Table II, cable

loss deviates more than in the full load case. This confirms

the needs to consider both longitudinal distribution of

current and time (load) dependence of power flow stated in

[1] for the loss evaluation of wind power. It also applies to

the other two industrial applications where the load

requirement changes dramatically over years.

One thing worth noting is that reactive compensation

plays an important role in the longitudinal current

distribution and in our case result, one-end compensation

is used. This causes larger differences in current between

the two ends of the long cable. Double-end compensation

shall give more balanced current and thus give smaller

difference in cable loss calculated with a constant

resistance (i.e. 𝑅2).

0 50 100 1500.075

0.08

0.085

0.09

0.095

0.1

0.105

cable length in kilometers

AC

res

ista

nce

in

oh

m/k

m

R1

R3

R2

0 20 40 60 80 100 120 140 16067

67.5

68

68.5

69

69.5

70

Cable length in kilometers

Vo

ltag

e m

agn

itu

de

in k

V

with R3

with R2

with R1

0 50 100 1500.005

0.01

0.015

0.02

0.025

0.03

0.035


Act

ive

po

wer

lo

sses

in

MW

/km

with R3

with R2

with R1

9




Figure 10. Voltage along the cable derived with different R – case result

2.

Figure 11. Power loss along the cable derived with different R – case

result 2.

C. Case Result 3– VSD Driven Motor with Long Cable

The third case result is derived for application of VSD

driven motor with long cable illustrated in Fig. 3. Results

are summarized in Table III.

Based on the results summarized in TABEL 3, a „wrong‟

resistance value 𝑅1 (15% deviation from „true value‟

according to Fig. 12.) may lead to very large differences in

voltage profile across the cable (10% deviation). Similarly,

the value of reactive power through the VSD is also

subjected to a large „error‟ due to large deviation of

voltage profile shown in Fig. 13. This provides more

evidence that the AC resistance value needs to be taken

care of in a well-controlled manner from the beginning of

engineering design, for this specific type of application.

Due to the fact that no reactive compensation is used in

such systems, current along the cable is quite balanced and

hence the longitudinal distribution of current is not critical

(difference between 𝑅2 and 𝑅3). This type of application

has variable voltage output (from VSD) to operate at

different loading. Therefore, the time (load) dependence of

power flow is not examined.

TABLE III. CASE RESULTS 3 – VSD DRIVEN MOTOR WITH LONG

CABLE

70km, 200Hz, 10MW, 5Mvar (full load)

52kV rated, 3×240mm2 cable

30kV operation


AC

resistanc

e

Cable send

end voltage

(kV)

Cable

receive end

voltage

(kV)

VSD var

(Mvar)

Cable

loss

(MW)

𝑹𝟏 30.49 27.28 5.80 1.130

𝑹𝟐 30.75 30.24 8.33 0.908

𝑹𝟑 30.75 30.29 8.36 0.904


Figure 13. Voltage along the cable derived with different R – case result

3.

Figure 14. Power loss along the cable derived with different R – case

result 3.

0 50 100 150

0.075

0.08

0.085

0.09

0.095

0.1


AC

res

ista

nce

in

oh

m/k

m

R1

R3

R2

0 20 40 60 80 100 120 140 16063.5

64

64.5

65

65.5

66

66.5

67


Vo

ltag

e m

agn

itu

de

in k

V

with R1

with R2

with R3

0 50 100 1500

0.005

0.01

0.015

0.02

0.025

0.03


Act

ive

po

wer

lo

sses

in

MW

/km

with R1

with R2

with R3

0 10 20 30 40 50 60 700.096

0.098

0.1

0.102

0.104

0.106

0.108

0.11

0.112

0.114


AC

res

ista

nce

in

oh

m/k

m

R1

R3

R3

0 10 20 30 40 50 60 70 8027

28

29

30

31

32

33


Vo

ltag

e m

agn

itu

de

in k

V

with R1

with R2

with R3

0 10 20 30 40 50 60 700.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022


Act

ive

po

wer

lo

sses

in

MW

/km

with R1

with R2

with R3

10



VI. FURTHER WORK

The practice for designing power system starts with

load flow sizing cable and reactive compensation strategy

(voltage regulations). Following this, fault calculation and

time domain simulations (EMTP type) are done to specify

protection and transient related parameters. The proposed

load flow scheme in this paper gives realistic pictures of

„pre-fault‟ states of the long cable transmission system and

the line resistances can be directly used in other

calculations following the load flow calculation.

Applications could also be extended to power system

operations.

Some other research work on submarine power cables

[10] raised questions about the loss calculation defined by

IEC 60287 based on measurements and finite element

methods. However, it is more product-oriented and an

analytical method facilitates the interface towards power

system engineering and it can be modified to meet

accuracy requirement.

Last but not least, the 3 types of industrial applications

discussed in the paper often involve large harmonic

contents due to the presence of power electronics. Current

harmonics in the cable results in additional conductor

heating hence higher conductor temperature [13]. This

factor is not considered in IEC 60287 but it can be taken

into account by superposition of temperature rise for the

specific harmonic orders, once derived from a harmonic

analysis.

VII. CONCLUSION

It is proposed that the IEC 60287 standard be directly

integrated into power system load flow in order to achieve

well-controlled results for the 3 industrial applications

with presence of long cables and/or variable frequency.

Case results have demonstrated the importance of AC

resistances. Wrong resistance value could lead to very

different voltage profiles (system design) and the

longitudinal distribution of currents along cable need to be

taken into account when the system is compensated at one

end and in particular for light load operation with long

cables.

The proposed load flow scheme integrates cable design

based on well-established standard with power system

design so that they are no longer decoupled processes by

themselves which reduces uncertainty and increases

observability of industrial power system design work.

Further work, such as the harmonic current superposition

can also be included in the thermal calculation.

ACKNOWLEDGMENT

The author would like to acknowledge the creators of

„MATPOWER‟, who facilitate research work in the area

of power system steady state operation, planning and

analysis work through open source programs.

REFERENCES

[1] H. Brakelmann, “Efficiency of HVAC power transmission from offshore windmills to the grid,” in Proc. IEEE Bologna Power

Tech Conference, 2003.

[2] N. B. Negra, J. Todorovic, and T. Ackermann, “Loss evaluation of HVAC and HVDC transmission solutions for large offshore wind

farms,” Elsevier Electric Power Systems Research, vol. 76, iss.11,

pp. 916–927, Jul. 2006. [3] R. D. Zimmerman, C. E. Murillo-Sánchez, and R. J. Thomas,

"MATPOWER steady-state operations, planning and analysis

tools for power systems research and education," IEEE Transactions on Power Systems, vol. 26, no. 1, pp. 12-19, Feb.

2011.

[4] H. Gedde, B. Slåtten, E. Virtanen, and E. Olsen, “Ormen lange long step-out power supply,” in Proc. Offshore Technology

Conference, 2009, paper OTC 20042.

[5] E. Baggerud, V. S. Halvorsen, and R. Fantoft, “Technical status and development needs for subsea compression,” in Proc.

Offshore Technology Conference, 2007, paper OTC 18952.

[6] G. E. Balog, N. Christl, G. Evenset, and F. Rudolfsen, “Power

transmission over long distances with cables,” in Proc. CIGRE

Session 2004, paper B1-306.

[7] T. Hezel, H. Baerd, J. J. Bremnes, and J. Legeay, “Subsea high voltage power distribution,” in Proc. IEEE PCIC, 2011.

[8] G. Scheuer, B. Monsen, K. Rongve, T. E. Moen, E. Virtanen, and

S. Ashmore, “Subsea compact gas compression with high speed VSDs and very long step-out cables,” in Proc. IEEE PCIC Europe,

2009.

[9] D. G. A. K. Wijeratna, J. R. Lucas, H. J. C. Peiris, and H. Y. R. Perera, “Development of a software package for calculating

current rating of medium voltage power cables,” in Proc. Trans.

IEE Sri Lanka, 2003 [10] R. Stølan, “Losses and inductive parameters in subsea power

cables,” M. Sc. thesis, Norwegian university of science and

technology, Trondheim, Norway, Jul. 2009. [11] Electrical Cables – Calculation of the Current Rating – Current

Rating Equations and Calculation of Losses, IEC60287-1-1,

2006-12. [12] Electrical Cables – Calculation of the Current Rating – Thermal

Resistance, IEC 60287-2-1, 2006-05. [13] A. Hiranandani, “Calculation of Cable Ampacities including the

Effects of Harmonics,” IEEE Industry Applications Magazine,

1998.

X. Yuan was born in Jiangsu, China in 1983. He

holds a BSc. and a MSc. degree (2005 and 2011) in

electric power engineering from Hohai University in China and the Royal Institute of Technology in

Sweden respectively. He started his professional

career with FMC Technologies in Norway in 2008 working on subsea power system projects. He

joined GE Oil&Gas Norway in 2010 and is now a

Lead Electrical Engineer in the Subsea Power Systems and Products department where he has been highly involved in the power system

design for subsea applications. His interest is in power system

engineering and power electronics. He has been a member of IEEE

since 2011.

G. Sande was born in Norway in 1964. He received

his MSc degree in 1987 and his PhD degree in

1993, both from Department of Electrical Power Engineering, Norwegian University Science and

Technology. In 1993 he took a position as

Researcher at ABB Corporate Research in Norway where he stayed until 2006. From 2006 to 2010 he

worked with development of electrostatic coalescer

equipment (oil-water separation) in Aibel Technology and Products. In 2010 he took a position as Senior Engineer in GE Oil & Gas, Subsea

Power Systems and Products where he has been leading several power

system studies, contributing to power product development and responsible for electrical testing technologies for GE Oil & Gas

Norway

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