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3.2 PNDR at Inner Grid
PNDR at inner grid is influenced by sum of the
number of faulted wind turbines and disconnected
wind turbines according to locations where cable
faults occur. Because of cable failure with a very
low probability, two or more cable failures are
ignored in this paper.
There are two different approaches to calculate
PNDR at inner grid based on the layouts. In case of
a layout of radial structure, PNDR is calculated by
ratio of the net disconnected wind turbines to the
total wind turbines, the net disconnected wind
turbines mean the union set consisting of the faulted
wind turbines and the disconnected ones. However,
in case of a layout of ring structure which has the
redundant cables, a more complex approach is
applied. When a failure occurs at one among feeders
composing a ring structure, power disconnected by
the cable failure would detour through the other
feeders in the ring structure. All the remained wind
turbines in the ring structure, except for wind
turbines connected normally toward offshore
substation in the faulted feeder may be limited
according to wind speed. If power to be delivered
through non-faulted feeders is higher than their total
rated capacity, the rated power of the wind turbines
is restricted as shown in Fig. 6.
Figure 6: Normal/Restricted Output Characteristic of WT.
Therefore, in case of layout of ring structure,
relationship between power delivered through non-
faulted feeders and their total rated power is
considered as well as the net number of
disconnected wind turbines. Equation related to the
limited rated power of wind turbine is represented
by Eq (1).
,
_
__
()
if)
.()
()
() ()
if)
.() .()
IG
IG IG
OS EG
rr
WT WT
rNew OS EG
OS EG OS EG
r
WT WT WT WT
ACap
N
ACap ACap
NN
f
PP
nn f
Pf
ff
nn f nn f
(1)
where,
OS EG
f
means failure state at offshore
substation and external grid and contains failure
factors at formal components,
()
OS EG
ACapf
is total
capacity of non-faulted feeders in a ring structure,
r
P
is the rated power of wind turbine,
WT
is the
number of wind turbines and
.
WT
nn
is the number of
the net disconnected wind turbines.
3.3 PNDR at Offshore Substation and
External Grid
Failure factors considered at two components affect
to PNDR of each component equally. Therefore,
Failure factors at two components are handled
together. Containing formal failure factors, failure
states can be defined by combination of faulted
transformers and external lines. If failures occur at
transformers and/or external lines, all wind turbines
may reduce their rated power only when power to be
delivered toward onshore from inner grid is higher
than the available capacity of offshore substation
and external grid. This process for determining the
limited rated power is same with case at inner grid
composed by ring structure.
After obtaining all PNDR under predefined
failure state at all components, an expected value of
PNDR is calculated by multiplying each PNDR and
the corresponding probability of failure state. And
then, an expected PNDR is used in order to evaluate
EEND. EEND is obtained by multiplying EPNDR
and an expected energy produced by the entire OWF
in non-failure state. This process is shown in Eq (2).
()Pr()
OS EG
OS EG OS EG
f
OWF
PNDR f f
EEND EE EPNDR
EENDC EEND asp
EPNDR
(2)
where,
Pr( )
OS EG
f
is probability of that the failure state,
OS EG
f
occurs.
OWF
EE
means an expected annual
energy of OWF in non-failure state and
asp
is an
average settlement price of electrical energy
generated by wind turbine.
4 CASE STUDY
In the section, brief case studies are performed in
order to demonstrate the proposed method. OWF is
composed by 28 identical 5MW-wind turbines.
Wind speed model is applied identically by
historical data model obtained at the southwest coast
in Korea. The expected annual energy of the entire
OWF is 367,159.6MWh considering no failures.
Basic alternatives based on layouts of inner grid
are represented by Fig. 7-9.
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