Integration of IEC 60287 in Power System Load Flow for

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

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. 

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.

Index Terms—load flow, variable frequency, submarine cables, subsea power, wind power, mat power, IEC 60287

II. I.

INTRODUCTION

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:

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].

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. Offshore wind Offshore Substation

Grid

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:

Manuscript received September 4, 2012; revised December 24, 2012. ©2013 Engineering and Technology Publishing doi: 10.12720/ijoee.1.1.6-11

PROBLEM FORMULATION

6


𝑷𝑳𝒐𝒔𝒔 =

𝑷𝑰𝒎𝒂𝒙 𝒍𝟎

∙

𝒍𝟎 𝑰𝟐 (𝒙) 𝒙=𝟎 𝑰𝟐 𝒏 (𝒙)

∙ 𝒗𝜽 (𝒙) ∙ 𝒅𝒙

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.

(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.

III.

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.

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. Subsea Switchgear

METHODOLOGY

Define Power System Topology Define Power System Parameters

Subsea VSD M

Onshore/Platform

STATCOM

Subsea transformer

Select Cable M

Long submarine cable

M

Loss Factors

Skin Effect

Cable Geometric Design Proximity Effect

M

AC Resistances L, C

Figure 2. Power distribution with long cable. Temperature Environmental Conditions

Current

Cable Ampacity

No

Cable Loading OK?

No

Voltage Profile OK?

Yes

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.

Newton Raphson Load Flow iterations Voltage & Current

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.

END

Topside VSD

Subsea Motor

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

M

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

Variable frequency over long cable

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 ©2013 Engineering and Technology Publishing

7


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.

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.

𝑸= U,Ɵ

𝑼(𝑼−𝑬) 𝑿𝑺𝑻

(2)

Controlled Bus

XST

E,Ɵ’

Additional Bus

VSC

IMPLEMENTATION

Figure 5. Steady state modeling of STATCOM.

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.

Correct implementation of reactive compensation is vital in such applications since it directly affects the current drawn in the cable.

A.

D.

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].

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.

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.

©2013 Engineering and Technology Publishing

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


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.

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.

Active power losses in MW/km

TABLE I.

0.035

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

AC resistance in ohm/km

with R1 0.025 0.02 0.015 0.01

50

100

150

Cable length in kilometers

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 30MVA onshore transformer, 30MVA subsea transformer

0.105 0.1

R1

0.095

AC resistanc e

0.09

R1 R2 R3

0.085

R3

0.08

R2

0.075 0

50

100

70 with R3 with R2

69.5

with R1 69 68.5 68 67.5

20

40

60

80

100

120

140

160

Cable length in kilometers Figure 7. Voltage along the cable derived with different R–case result 1.


Cable end voltage (kV) 66.01 66.65 66.59

STATCO M (Mvar) 28.42 28.77 28.73

STATCO M voltage -0.0953 pu -0.0953 pu -0.0953 pu

Cable loss (MW ) 1.537 1.194 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 ).

150

cable length in kilometers Figure 6. AC resistances along the cable (R 1 , R 2 and R 3 ) – case result 1.

Voltage magnitude in kV

3

with R2

0.005 0

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 𝑅3 as „true‟ value, the cable end voltage has nearly 1kV deviation with approximately 20% difference in resistance (𝑅1 ).

67 0

with R 0.03

9


has variable voltage output (from VSD) to operate at different loading. Therefore, the time (load) dependence of power flow is not examined.


0.1

R1

0.095

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

0.09 0.085

70km, 200Hz, 10MW, 5Mvar (full load) 52kV rated, 3×240mm2 cable 30kV operation 30MVA onshore transformer, 15MVA subsea transformer

R3

0.08 0.075

R2

0

50

100

150

Cable length in kilometers Figure 9. AC resistances along the cable (R 1 , R 2 and R 3 ) – case result 2. 67 1

66.5

with R

2

with R

3

66

Cable send end voltage (kV)

𝑹𝟏

30.49

Cable receive end voltage (kV) 27.28

𝑹𝟐

30.75

𝑹𝟑

30.75

65.5

0.114

65

0.112



with R

AC resistanc e

64.5 64 63.5 0

20

40

60

80

100

120

140

160

Cable length in kilometers

Figure 10. Voltage along the cable derived with different R – case result 2.

VSD var (Mvar)

Cable loss (MW)

5.80

1.130

30.24

8.33

0.908

30.29

8.36

0.904

R1

0.11 0.108 0.106 0.104 0.102 0.1

R3

R3

0.096 0

0.03 1

with R

0.025

10

20

30

40

50

60

70

Cable length in kilometers Figure 12. AC resistances along the cable (R 1 , R 2 and R 3 ) – case result 3.

with R

2

with R

3

0.02 33 with R1

0.015



0.098

0.01 0.005 0 0

50

100

150

Cable length in kilometers Figure 11. Power loss along the cable derived with different R – case result 2.

2

with R

3

31 30 29 28 27 0

10

20

30

40

50

60

70

80

Cable length in kilometers Figure 13. Voltage along the cable derived with different R – case result 3.

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


C.


with R

32

0.022 with R

1

0.02

with R

2

with R

3

0.018 0.016 0.014 0.012 0.01 0.008 0

10

20

30

40

50

60

70

Cable length in kilometers Figure 14. Power loss along the cable derived with different R – case result 3.

10


VI.

[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.

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.

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

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


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Integration of IEC 60287 in Power System Load Flow for

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