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Systematic Description of Dynamic Load for Cables for Offshore Wind Farms.
Method and Experience
Conference Paper · August 2016
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CIGRE 2016
Systematic Description of Dynamic Load for Cables for Offshore Wind Farms.
Method and Experience
Thomas KVARTS, Ivan ARANA
DONG Energy Wind Power
Denmark
Rasmus OLSEN, Poul MORTENSEN
Energinet.dk
Denmark
SUMMARY
With the increasing size of offshore wind farms, the number of array and export cables are
also increasing. Since the cost of cables contribute significantly to the cost of offshore wind
farms, there is an increased focus on improving the transfer capability of each cable, thus
reducing the cross section or even the number of cables.
It has been seen from Distributed Temperature Sensing (DTS) measurements that cables
installed for offshore windfarms, designed for continuous load, rarely reach their expected
service temperature calculated at steady state. This especially applies to areas with deep
burial, which, to a large extent can be explained with the thermal capacity of the surrounding
soil when the dynamic nature of the load in cables have not been considered [1].
This paper suggests a systematic method of describing the dynamic load from offshore wind
farms ending up with a “worst-case dynamic load profile” that with a simple step load curve
together with the thermal properties of the surroundings, provides an unambiguous design
basis for cable sizing/rating. This can be further used in simple dynamic Finite Element
Method (FEM) models by cable manufacturers or designers to model the cable installation
conditions. The method is a development of the method presented in CIGRÉ TB610 [2]
appendix D.5.
To further justify the method, a Thermoelectric Equivalent (TEE) model, [3], is used to
calculate the maximum cable temperature on the actual input load data for the worst year
available as well as the found worst-case load profile. The TEE is used since it is an analytical
numeric solution that can quickly calculate the temperature response even for detailed load
data corresponding to several years. The TEE model has previously been compared to FEM
and laboratory measurements [3]-[4] but a comparison between the TEE model and site
measurements from an offshore wind farm is presented as a novelty in this paper.
KEYWORDS
Dynamic Load, HV Cables, Submarine Cables, Wind Power, Thermal Resistivity,
Thermoelectric Equivalent, TEE.
thokv@dongenergy.dk
Background
The work presented in this paper is a continuation of the method for describing the dynamic
load of a wind farm, presented in CIGRÉ Technical Brochure 610 Offshore Generation Cable
Connections, appendix D.5 [2]. The method has been used by the Danish TSO Energinet.dk to
specify the cable for the “Horns Reef 3” 400 MW offshore wind farm, where a “worst case
load even” was found by subjecting the load data to a moving averages analysis. The
assessment of the data was mainly performed intuitively, based on knowledge of thermal
constants of a buried cable system, and print out of a large number of running averages. This
simple approach was possible since the amount of data was limited to only 3.5 years and
because results could be compared and partly confirmed by service experience with the
nearby offshore windfarm “Horns Reef 2”.
In the following, the same methodology is developed further, giving a more automated and
reproducible approach to choose appropriate length of time steps and how to exclude
irrelevant data. This development gives the cable designer an easy way to find the length of a
final full load period and a way to exclude short full-load periods in the running averages of
preceding longer-low load periods, as well as to identify few critical years to investigate in
depth.
Worst-case dynamic load profile
A load pattern of a cable for a wind farm can be directly related to the wind speed by the wind
farm power curve, see example in figure 4-14 in CIGRÉ TB610 [2]. It has in the recent years
become possible to obtain many years of detailed historical wind data, modelled or measured,
even for offshore areas, with resolution down to 10 minutes. It is therefore now possible to
analyse the cable load data in detail prior to specifying and selecting the cable.
The advantage of using historical wind time series, rather than wind statistics, is that the
nature of the wind is captured better. This means that both the yearly variations, as well as the
short duration characteristic of the weather systems consisting of low and high pressure
systems following each other in succession, are seen.
It is for example easily concluded, from such wind data, that it is unlikely for an offshore
wind farm to experience more than 5-7 days of continuous full production if such an event has
never happened in 16 years.
These aspects should be included in the design criteria used for dimensioning cables, in an
unambiguous way, that when used together with the thermal characteristic of the surroundings
enable different suppliers to achieve the same results.
The “Worst case dynamic load profile” as found in the following, is an attempt to provide
design criteria based on the dynamic load of a wind farm utilising the thermal capacity
(inertia) of the surroundings of the cables for improved cable rating:
Long term running RMS
A base tool, used in the method is long term running RMS (Root Mean Square) of load
values, that will be used instead of just running average load throughout this document in line
with the CIGRÉ TB 610, [2] example. This is due to the fact the heat losses of a cable is
mainly proportional to the current squared. These running RMS load values are found as a
function of start time and length of the period according to (1).
1
𝑡=𝑡 +𝑇 2
𝐼 (𝑡)𝑑𝑡
𝐼𝑅𝑀𝑆 (𝑡𝑠 , 𝑇) = √ ∫𝑡=𝑡 𝑠
𝑇
𝑠
(1)
2
Where:
t is the time, ts is the start time, T is the length of the RMS period over which the heating of
the cable by the current must be found (e.g. 7 days, 14 days, 20 days, 40 days, 70 days…) and
I(t) is the load current as function of time based on historical wind data and the park power
curve.
Reactive power (charging current) at the location of the cable route where hot spot is expected
could be included. But since it can be shown that the heat loss contribution of a constant
reactive power is independent of the load current, it is recommended to ad this late in the
process, since it will vary with capacitance of the final cable design and solution for reactive
compensation. It could even be left up to the cable manufactures to include the reactive power
based on a given reactive power compensation setup. It should however be noted that the
reactive power may not be fully independent of the park load.
Step by step method for generating a Worst case dynamic load profile:
1. A useful first step in analysing the data has been found to be plotting the maximum
running RMS load current (as function of the period T) using (1).
a. Data on historical wind speed and wind direction of the farm w(t) are gathered for
as many years as possible.
b. The wind farm power curve P(w) including wake losses is found or estimated
c. The load current in the cable is found as a function of the produced power, and the
expected voltage, I(P, U).
d. From w(t), P(w) and I(P,U) the running (RMS) load current is IRMS(ts,T) is
calculated for different periods T (1 day, 2 days… up to 60-100 days), with
starting times ts in each data point for the entire data set, e.g. each 10 min or 1 hour
(data sets of 1 hour resolution should be sufficiently accurate). For each period T
the maximum value is found. These maximum values can now be presented as a
function of T, in Figure 1.1
7 days
10 days
40 days
Figure 1; Example of maximum wind farm load in percentage for a future offshore windfarm in the UK
as a function of the period T, based on 16 years of historical wind data modelled for the windfarm
location.
2. From Figure 1 the relevant periods T to investigate further can be found by looking for
step changes in the graph. This part of the analysis will require some experience, but
1
In the example the charging current has at this point not yet been included
3
the most important last step change of the “worst case load profile” (Figure 5 (b)) x
days of 100 % load is found quite easy from this figure (step a. below):
a. It is seen that it is unlikely to ever have more than T=7 days of 100 % load since
the highest 7 day RMS value for 16 years is already fallen to 98%.
b. The next significant step change is at T=10 days where the RMS drops to 96%,
c. The final step change found from the graph is at T=40 days,
d. No more T values have been deemed necessary since the final 3 steps will describe
the last 57 days (40+10+7 days) of the worst case load profile, which exceed the
length of the most windy part of the winter periods of the investigated years, and a
RMS value for the entire data set of 16 years can be used for the preceding steady
state initial value.
e. The number of step changes to use could be refined to improve the effect of the
method if needed, but in the example shown in Figure 1 identifying 3 step changes
has for the worst case load profile, been seen to be sufficient to get a significant
rating improvement.
3. The time periods T (here 7, 10 and 40 days) found in the previous procedure (2) are
used to calculate and plot the RMS current for the entire data set provided (16 years),
to identify the most windy years to be analysed further. If a few most windy years
(winters) cannot be identified from this, additional periods could be analysed (e.g. 17
(7+10) or 47 (17+40) days). An example for T = 40 is shown in Figure 2 (i.e. running
IRMS(ts,T=40 days) for 16 years), where the two peaks for year 10 (I4010) and 15
(I4015) can be selected for further analysis. This can be repeated for the other chosen
periods T since additional worst years may need to be investigated.
Figure 2; Running IRMS(ts,T=40days) for 16 years, the two peaks identified for year 10 (I4010) and 15
(I4015) to be analysed further (the charging current from an assumed worst case location on the cable
route is included at this time but this could have been omitted and added later)
4. Since it is often the case for IRMS(ts,T) that a T=10 days maximum includes the 7 days
maximum, and that the T=40 day maximum includes the T=10 and the T=7 days
maximum, for each of the years suspected to be worst case years, the following
“punch out procedure” is to be performed so that several events are not included more
than once in the worst case load profile:
f. The running IRMS p.u. values are plotted and the maximum values for each
duration period T (7, 10 and 40 days) are identified (see Figure 3 A, B, C)
4
A
B
C
Figure 3; Square 1 hour current (I2), 7 days (I7), 10 days (I10) and 40 days (I40) running RMS currents as
function of days in year 15. The x-axis shows the days starting from the first year.
g. The data preceding the maximum running RMS value for the lowest duration
period (T=7 days) is removed (blue area of Figure 4) and the new running RMS
apparent currents are plotted (dashed lines in Figure 4) as if the data for the 7 day
period was not there, (both time and value removed from the data set so the RMS
values can be found across/on both sides of the removed period).
h. The new residual maximum values for each duration period are located; in Figure
4 it is seen that the T=10 days year-15 maximum is reduced from 0.98 to 0.96 (red
Δ).
i. The data preceding the maximum value for the second lowest duration period
(T=10 days) is removed (red area in Figure 4) and the new running RMS apparent
currents are plotted (dotted lines in Figure 4).
j. The new residual maximum values are located; in Figure 4 it is seen that the T=40
days year-15 maximum is reduced from 0.93 to 0.88 (green Δ).
Figure 4; Original 7 days (I7), 10 days (I10) and 40 days (I40) running RMS currents (solid lines) as
function of days in year 15, after removing the worst 7 days (dashed lines) and after removing the worst 7
+ 10 days (dotted lines). The x-axis shows the days starting from the first year.
5. Step 4 is repeated for every selected (windy) year and the maximum RMS current
values found for each period in all selected years.
6. The steady state preload used is found as the RMS value for the entire period with data
available, but cut to include only whole years. In this case 0.74 p.u. (not included in
5
Figure 4) It could be considered to specify the preload time to be limited to the
lifetime of the windfarm e.g. 25 years, but the improving effect on cable rating is
negligible except for very large burial depths.
7. Finally, the Worst-case dynamic load profile as a step change curve is produced from
the previously found residual maximum load for each duration period and investigated
windy year, see Figure 5 (b)
Example of step 7 performed on year 15:
Discussion of data
Figure 5a) shows the RMS load current after the 7 days (blue area) and 10 days (red area)
periods have been removed, and the 40 days period, used to calculate RMS current with
T=40, is shown with a green area.
Discussion of data
Figure 5b) is the end result of the method, i.e. the worst case dynamic load profile that serves
as input to manufacturer calculations used for cable dimensioning. In Figure 5b) it is possible
to see how steady state preload (step 6) is followed by the 40 days period (green area), the 10
days period (yellow area) and finally 7 days period (blue area).
This is a conservative approach in the example, since the order of events (the step changes)
are shifted in time so that the 3 blocks representing 7, 10 and 40 days are in the most
unfavourable order with the highest wind at the end of the Worst case dynamic load profile.
This reverse order has shown to be the case in all analysed locations so far, where the wind
has shown to be more consistent in the fall before the windy winter period, than in late
winter/spring. By shifting the order, it is considered that the method includes the odd
possibility of having a consistently windy event in late winter/spring, sometime in the future.
But if this was not the case, it should be considered to include another margin of security in
the method, if dynamic loading is not combined with e.g. online temperature and load
monitoring.
Wind farm load and RMS current in p.u.
Square current and RMS current in p.u.
T=7
T=10 1.00
0.96
T=40
0.88
Preload
T=∞
0.74
(a)
(b)
Figure 5; (a) Running RMS current during an investigated year and (b) Maximum values for all years as
a sums up to a Worst case dynamic load profile in p.u. as a function of days (red curve). (Charging
current of a specific location on the cable route is included). The coloured blocks in (a) and (b) represent
the same areas. In (a) the x-axis shows the days starting from the first year.
Discussion of data
For this example, the wind farm power curve including aerodynamic wake losses have been
used. Depending on the site weather conditions, wind turbines and wind farm layout the wake
losses become irrelevant after 16-17m/s as all turbines operate at rated capacity. Additionally,
no power curtailment or turbines out of operation were assumed.
6
The historical wind speed and direction of the farm data sets have 1 hour resolution, this has
been deemed sufficiently accurate to represent the load variations from a large wind farm and
temperature variations to accurately calculate the long term running RMS values. Other faster
temperature or loading variations do not need been accounted for since any maximum final
temperature will be only seen after several days off full load due to the long thermal constants
of the cable surroundings and represented by the last step of the Worst case dynamic load
profile.
Thermoelectric equivalent
For analysing the thermal response, of an export cable, to the Worst case dynamic load profile
the Thermoelectric Equivalent (TEE) method may be used. TEE is a simple but very time
efficient method, to model the thermal response of a power cable to an applied load. The
method is based on the resemblance between heat flowing in a thermal system (such as a
cable installation) and the current flowing in an electric circuit. The analyses of the
temperature at different positions in cables thus rely on simple algebra, which is why TEE
calculations are fast compared to other methods. Different studies, [3]-[8] have shown that the
TEE method, even though it is simple, can model the dynamic temperature in a power cable
very accurately, i.e. within a couple of degrees centigrade.
By applying the TEE method, to a static load and to the load of Figure 6b), it can therefore be
compared how large a conductor is needed when 1) dimensioning export cables based on
steady state requirements and 2) dimensioning export cables based on the Worst case dynamic
load profile.
In the simulations the parameters in Table 1 have been used.
Parameter
L
ρtherm,soil
θamb
ctherm,soil
Value
2.0
0.7
10
2∙106
Unit
m
K·m/W
°C
J/(K·m³)
Description
Installation depth, centre of cable
Thermal resistivity of seabed
Ambient temperature
Specific heat of seabed (low estimate!).
Table 1; Thermal parameters of surroundings
As the dimensions and designs of three phased HV cables may vary from manufacturer to
manufacturer, the dimensions in Table 2 have been used in the simulations.
Parameter
dc
di
ds
dj
da
De
Wd
λ1
λ2
ks
kp
Value
41.5
91.0
101.0
107.4
248.9
261.9
0.8
0.3607
0.3573
1.0
1.0
Unit
mm
mm
mm
mm
mm
mm
W/m
-
Description
Conductor diameter
Insulation outer diameter
Lead sheath outer diameter
Outer diameter of each cable core
Armour outer diameter
Cable outer diameter
Dielectric losses
Screen loss factor. As per IEC 60287
Armour loss factor. As per IEC 60287
Skin effect coefficient
Proximity effect coefficient
Table 2; Cable dimensions used in the simulation of static and dynamic thermal response to loads.
7
Even though it is a simplification, the dimensions in Table 2 have been used for all conductor
cross sections, where adaption in relation to cross section has been made only in the electrical
resistance of the conductor. I.e. the thermal simulations have taken into account the lower
electrical resistance of a larger conductor by utilising the resistances stated in IEC 60228, [9].
The projected current profile for a 220 kV export cable from a specific wind farm location
looks as shown in Figure 6a), where the maximum current is 1052 A. The worst case load for
this profile is shown in Figure 6b).
a)
b)
Figure 6; Current used in the TEE calculations with the (a) actual current for the worst year found (year
15) and the given (b) Worst case load profile. Both loads include charging current for a specific location
on the cable route.
Under conventional, steady state, dimensioning of the export cable, a 1052 A requirement
would necessitate the installation of a 2000 mm2 aluminium conductor cable whereas the
dynamic loading profile in Figure 6b) only necessitates the installation of a 1600 mm2
aluminium cable as shown in Figure 7.
Figure 7; Thermal response of a 1600 mm2 3-phased submarine cable to worst case dynamic load profile
in Figure 6b).
Comparison between worst case dynamic load profile and dynamic load by TEE
The simplified worst case dynamic load conditions of Figure 6b) was, as stated, derived from
Figure 6a) as it is easier for the cable buyer to compare the performance of cables from
different manufacturers, during tendering phase, when the load conditions are simplified.
8
In order to show that the simplification approach is also thermally valid, the thermal response
of a three phase export cable to the load profiles in Figure 6a) and Figure 6b) is compared in
the following.
The thermal analyses of Figure 8 show that the Worst case dynamic load profile seems to be
on the safe side when comparing to the original load profile as the maximum temperature of
the conductor in the two cases is 88 °C (Figure 8b)) and 85 °C (Figure 8a)) respectively. This
suggests that it might be possible to use an even smaller conductor and still respect the
general 90 °C limitation of XLPE cables.
a)
b)
Figure 8; Thermal response of a 1600 mm2 3-phased submarine cable to a) originally predicted load
profile and b) worst case dynamic load profile
Furthermore, if the final step of 1p.u. (full load) for 7 days in the Worst case dynamic load
profile would last less days, it could be possible to decrease the cross section of the cable even
further.
The thermal response of a 1400 mm² aluminium conductor cable, to the originally predicted
load of Figure 6a), results in a maximum conductor temperature of approximately 95 °C
which is not acceptable. However in case the buyer allows the use of an off-standard cross
section, a conductor of 1500 mm² aluminium would result in 90 °C.
By changing the dimensioning criteria from a steady state load to the varying load it is
therefore possible to reduce the conductor cross section by 25 %.
Comparison between TEE and FEM
As the TEE method by nature is a very simplified 1D model of the 3D reality, it should be
tested how the method performs compared to more extensive simulations. The present section
is therefore dedicated to comparing the results of TEE simulations with 2D FEM simulations.
As shown in Figure 9 the TEE method is accurate within ± 2 °C, for almost the complete
simulated time period, when comparing to the FEM simulations, and this is even though the
simulation time of the TEE method is 10 seconds which is approximately 50 times faster than
the FEM simulations. For additional information regarding FEM and TEE calculations, please
refer to [3].
9
a)
b)
Figure 9; Comparison of TEE method and FEM simulation. a) Absolute comparison and b) difference
between simulation results.
It should be acknowledged that it is difficult to obtain a more accurate result with a method
which simulates the complex structure of a three phased export cable in one dimension. In its
nature the TEE method simulates the thermal system as if it consisted of cylinders, which of
course is difficult when the cable consists of three phases configured in a triangular geometry.
Furthermore, it should be acknowledged that in order to utilise thermal simulations not only
in dimensioning but also in the operation of the three phased cables, i.e. utilising Dynamic
Line Rating, it is necessary to have simple and fast simulation tool which can be implemented
in IT systems already existing at power grid operators (such as SCADA systems). The TEE
methodology is ideal for such applications as it requires a minimum of computational
resources and relies on well-known algebra. This could be interesting for wind farm
operators, since implementing the dynamic load method for cable design, may also encourage
to design the cables with the possibility to curtail the power from the wind farm, since the
method easily could be used to assess how often curtailing would be necessary over the life
time of the wind farm.
Relevant DTS measurements
This section is dedicated to comparing the TEE simulation of a three phase cable with
measurements obtained from the transmission grid.
Figure 10a) shows measurements of the highly varying current output of an offshore wind
farm from when the first turbines are installed and the following almost two years. Figure
10b) shows measurements of the temperature in the fibre (red, dotted line) and the TEE
method simulated temperature (blue, solid line).
10
a)
b)
Figure 10; a) Measurement of load b) Measurement and TEE method simulation of temperature of the
fibre.
It is seen that there are some deviations between the measurements and the TEE method
simulations; however this should be seen in the light that it has not been possible to gain
access to credible data for the surrounding temperature. The simulations have therefore been
performed by assuming constant 10 °C surroundings, and this of course affects the accuracy
of the simulations when comparing to the measurements. On this background it should be
recognised that the TEE method simulations are accurate within ± 8 °C, even with the lack of
information regarding the ambient temperature, and this must be considered very satisfactory.
From the above it is obvious that greater knowledge of the ambient conditions would lead to a
better forecast of the loadability of the cable as mentioned as well in [10]. Measurements of
the ambient temperature in the seabed, as well as measurements of the thermal resistivity and
heat capacitance, are therefore recommended to be performed wherever possible. It may even
be that some meteorological databases (or Geographical Information Systems) already contain
such information and such datasets should therefore be sought for.
Conclusions
This paper proposes a step-by-step methodology to sort several years of data of wind speed
and direction, to calculate RMS currents and finally a worst-case dynamic load profile. Here,
a sequence of loads with different durations are increased gradually until the maximum load is
reached. This simple load profile allows the supplier to design the cable.
Subsequently, the conductor temperature is calculated using the predicted load profile and
worst case dynamic load profile. Here, the final conductor temperature shows small
differences, using both loads. The paper continues to compare the TEE model with FEM
simulations. The paper finishes with a comparison of measurements and TEE simulation; the
results to show fair agreement.
It is shown that application of dynamic loading is relevant when large export cable systems
are operated with varying load, allowing for a reduction of the conductor cross section in the
range of 25 % compared with a continuous loading. In principle the procedure can be used for
both underground and submarine cables; however the installation conditions along the route
would determine the dynamics of the cable system and hereby the effect of utilising dynamic
loading for cable rating and especially cable routes with deep burial will benefit of from
dynamic loading.
11
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