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Probabilistic Reliability of HVDC Expansion Planning in South Korea
Jaeseok ChoiGyeongsang National University
1
ORCID ID : 0000-0003-0867-6251
Composite System Reliability TF
Aug. 08, 2019
2
South Korea
Atlanta
Background The energy paradigm worldwide is shifting to one that prioritize reduction of
carbon since Paris Agreement. In addition, the conversions into renewableenergy sources as well as into grid connection are also progressing rapidly.
The theory is provided for more rational planning by considering theuncertainty of wind turbine generators (WTGs), which have highly variableoutput, as well as the forced outage rates (FOR) of generators, transmissionlines, and HVDC.
This paper proposes composite power system reliability evaluation usingCMELDC (Composite Power System Equivalent Load Duration Curve) (Nodaleffective load model). This paper considering uncertainties model (Multi-state)of WTG.
This study also proves the efficiency of the proposed method by applying it topractical HVDC expansion planning (between mainland and Jeju island) for Jejuisland power system in South Korea.
3
4
Reliability Evaluation at HLII including WTG
The HVDC expansion plan is one of the grid plans. Therefore, it is not
easy to evaluate the reliability of HLII including the transmission system.
Fig. 1. Hierarchical structure for
reliability evaluation of power system
Generation System
Transmission System
Distribution System
HL I
HL II
HL III
1) HLI Effective Load Model
(a) Actual system (b) Equivalent system
5
k Lx
~
~
~
~
Trans.
System
2 2, tCT q
, i tiCT q
, NT tNTCT q
1 1, tCT q
WTG1, go1
CG2, go2
CGi, goi
CGNG, goNG
)(ojosik
xf
Lkx
Lkx
Lkx
Lkx
Lkx
1
1
ik
ik
qAP
2
2
ik
ik
qAP
ijk
ijk
qAP
iNSk
iNSk
qAP
sijk
sijk
q
AP
where,CG, CT: capacity of Generator and transmission lineq, qt: The FOR of each generator and transmission lineAPij: Capacity at any load point
Fig. 2. Actual system
Fig. 4. Synthesized fictitious equivalent generator
WTG1, go1=0
CGNG, goNG=0
k Lx
~
~
~
~
k oNGjx k NGj
k NGj
AP
q
Trans.
System
2 2, 0tCT q
, 0i tiCT q
, 0NT tNTCT q
1 1, 0tCT q CG2, go2=0
CGi, goi=0
Fig. 3. Equivalent system
2) HLII Effective Load Model
6
3) Reliability indices at the load points(buses)
The reliability index in HLII calculates the power system and individual
reliability indices. First, the reliability index at the load point can be formulated
as follows Eq. (1) to (3) using the effective load probability distribution function
as follows.
※ In the index of LOLE and EENS, the lower is better.
( )k
k k NG x APLOLE x
(x) dxk pk
k
AP L
k k NGAP
EENS
1 k
k
k
EENSEIR
DENG
(1)[hours/yr]
(2)
(3)
[MWh/yr]
[pu]
where,Lpk: peak load at load point k[MW]APk: maximum arrival power at load point k[MW]
)( NGk
kLOLE
PkL kAP kPk APL
kEENS
[MW]
Time
)( Ok
CMELDC
LDCT
7
4) Reliability indices of the bulk system (Composite power system)
While the EENSHLII of a bulk system is equal to the summation of the EENSk at
the load points as shown in Eq. (4), the LOLE of a bulk system is entirely
different from the summation of the LOLEk at the load points. Fortunately,
because the ELCHLII (Expected load curtailed) of bulk system is equal to the
summation of ELCk at the load points as shown in Eq. (5), an equivalent defined
LOLEHLII of the bulk system can be calculated using Eq. (6).
1
NL
HLII k
k
EENS EENS
1
NL
HLII k
k
ELC ELC
/HLII HLII HLII
LOLE EENS ELC
1 k
k
k
EENSEIR
DENG
[hours/yr]
[MWh/yr]
[MW/cur.yr]
[pu]
(4)
(5)
(6)
(7)
where,
NL: Number of load points
ELCk = EENSk/ LOLEk
DENGk: Demand energy at bus #k
8
MULTI-STATE OPERATION MODEL OF WTG
Fig. 5 shows the relationship between the power output of a WTG and the
wind speed, where, Vci is the cut-in speed[m/sec], VR the rated speed [m/sec],
Vco the cut-out speed [m/sec], and PR the rated power [MW].
1) WTG Power Output Model
Fig. 5 A typical power output model of WTG
9
Wind speeds vary both in time and space. It has been reported that the actual
wind speed distribution can be described by a Weibull probability distribution
and approximated by a normal distribution. This study uses the normal
probability distribution function to model the wind speed in terms of the mean
wind speed value μ and the standard deviation σ as shown Fig. 6.
Fig. 6 The common wind speed model
2) Wind speed model
2 3 4 5 2 3 4 5
0m/s Wind speed [m/sec]
10
3) Multi-state model of WTG using normal PDF
Fig. 7 combines the typical output characteristic curve of the WTG with the probability
distribution function of the wind speed model. Then, a linear graph of the probability
according to the output of the wind turbine generator can be drawn using Fig. 8.
Fig. 7 Components of a model describing the power output states of a WTG and the corresponding probabilities
Fig. 8 Linear graph of power and probability of WTG
Here,PM : Output of WTG for wind speed M[m/sec]PBM : Probability of wind speed model for windspeed M[m/sec]μ : mean of wind speedσ : standard deviation of wind speed
Wind speed [m/sec]
[ ]Power MW
( , )M MP PB
( , )i iP PB1 1( , )i iP PB
2 2( , )i iP PB
2 3 4 5 2 3 4 5
0 m/s
Wind speed [m/sec]
11
The probability of output is obtained and rewritten to the same output interval using
linear interpolation as shown in Fig. 9 and Eq. (8), (9).
Fig. 10 shows the multi state probability distribution function of a typical WTG thus
obtained and satisfies Eq. (10).
Here, NS is the number of operation states of the WTG, the rated output PR is PNS-1.
Fig. 9 Graph using linear interpolation accordingto Fig. 8 for same interval
Fig. 10 The typical multi states probability distribution function of WTG output using Fig. 9
1k i
k i
P PPB PB
P
1
i k
k i
P PPB PB
P
1 1( , 1, 2,..., 2)
i i i iP P P P P i NS
단
(8)
(9)
(10)
12
Fig. 11 is a structural diagram for evaluating the reliability of the elements constituting
the HVDC. As shown in the figure, the FOR of the whole HVDC is a serial connection, so it
is formulated as Eq. (11).
HVDC HVDC ct DCL csFOR = q = (1-(p p p ))
=( ( ( ))( ( ))( ( ))1 1 / 1 / )1 /ct ct ct DCL DCL DCL cs cs cs
[f/ yr]
[hour]
ct
ct
Terminal
Station
Terminal
Station
Rectifier InverterDC Line
Shunt
Ground
Shunt
Ground
[f/ yr]
[hour]
DCL
DCL
[f/ yr]
[hour]
cs
cs
(11)
Fig. 11 Reliability Evaluation Model of HVDC
Here,
λct, λDCL, λcs: Failure rate of converter, inverter and DC cable to the HVDC components
μct, μDCL, μcs: Repair rate of converter, inverter and DC cable to the HVDC components
RELIABILITY EVALUATION MODEL OF HVDC
13
In this paper, to verify the effectiveness of the proposed reliability evaluation method, a
Jeju island power system including three wind farms(HWN, HLM, SSN) was used as
shown in Fig. 12. It is assumed that the #1, #2 HVDC line is already installed and the #3
HVDC line is scheduled to be installed.
- Peak load is 681 [MW], 11 buses, Load point 7
Fig. 12 Model system for reliability evaluation
Case Study
14
The load variation curve of Jeju island power system is shown as Fig. 13 The windspeed variation curve of Jeju island power system is shown as Fig. 14
Fig. 14 The wind speed variation curve of Jeju island power system
Fig. 13 The load variation curve (pattern) of Jeju island power system
15
Name TypeCapacity
[MW]
Nu
m
α[Gcal
/MW2h]
β[Gcal
/MWh]
γ[Gcal
/hour]
Fuel
Cost (f)
[$/Gcal]
FOR
1HVD
CDC 75/150 2 0.004 1.512 45.207 43.300 0.028
2 NMJ3 T/P 100 2 0.004 1.512 45.207 43.300 0.012
3 JJU1 T/P 10 1 0.062 2.100 5.971 43.599 0.015
4 JJU2 T/P 75 2 0.003 1.832 30.231 43.599 0.012
5 HLM1 G/T 35 2 0.004 2.401 20.320 77.909 0.013
6 HLM1 S/T 35 1 0.004 2.401 20.320 77.909 0.013
7 JJU3 D/P 40 1 0.025 0.364 28.484 43.599 0.018
8 NMJ1 D/P 10 4 0.006 1.999 1.360 43.300 0.018
Haengwon Seongsan Hanlim
WTG capacity 50 MW 30 MW 20 MW
Cut-in speed(Vci) 5 m/s 5 m/s 5 m/s
Rated speed(VR) 16 m/s 15 m/s 14 m/s
Cut-out speed(Vco) 25 m/s 25 m/s 25 m/s
Table 1. GENERAL GENERATOR CHARACTERISTIC DATA
Table 2. Wind Farm characteristic data
Num Name Type Start Bus End BusCapacity
[MW]FOR
1 HWN1 WTG 0 10 50 0
2 SSN1 WTG 0 9 30 0
3 HLM1 WTG 0 4 20 0
4 HVD1 HDC 0 1 150 0.028
5 HVD2 HDC 0 1 150 0.028
6 HVD2 HDC 0 1 150 0.028
7 NMJ3 T/P 0 5 100 0.012
8 NMJ4 T/P 0 5 100 0.012
9 JJU1 T/P 0 1 10 0.015
10 JJU2 T/P 0 1 75 0.012
11 JJU3 T/P 0 1 75 0.012
12 HLM1 G/T 0 4 35 0.013
13 HLM2 G/T 0 4 35 0.013
14 HLM1 S/T 0 4 35 0.013
15 JJU3 D/P 0 1 40 0.018
16 NMJ1 D/P 0 5 10 0.018
17 BUDG T/L 1 2 300 0.001713
18 BUDG C/L 1 2 200 0.001
19 DOSN T/L 2 3 200 0.00571
20 HAJU T/L 3 4 200 0.001142
21 HALM T/L 4 6 200 0.001142
22 SAIN T/L 3 6 200 0.001142
23 SISG T/L 6 7 200 0.001142
24 NAJE C/L 5 6 226 0.001
25 NAWN T/L 7 8 200 0.00571
26 ANDK T/L 6 8 200 0.001142
27 HASG T/L 8 9 200 0.004568
28 HALA T/L 8 1 200 0.001142
29 HGWN T/L 1 10 200 0.004568
30 JOSG T/L 10 9 200 0.001142
31 JOSG C/L 2 11 220 0.001
Number Name Bus NumberCapacity
[MW]
1 JEJU 1 130
2 SIJU 1 161
3 SEGP 1 111
4 HALA 1 68
5 SUSN 1 74
6 HALM 1 19
7 SAJI 1 56
Table 4. Transmission data of Jeju island power system
Table 3. Load data of Jeju island power system
1) Input Data
16
#1 HVDC is fixed in the connection of bus
#1 and #2 HVDC is assumed to link at bus
#11 because it was the best case in terms
of reliability compared to other candidates.
Table 5 shows the results of reliability
evaluation for the model system.
HVDC #2
Grid not
constrained
Grid
constrainedBus #1 Bus #4 Bus #10 Bus #11
LOLE
[hours/year]1.26 6.89307 0.403583 0.403584 0.397534 0.097253
EENS
[MWh/year]44.52 3587.35 231.596 231.596 228.625 55.283
EIR
[pu]0.99999 0.999222 0.99954 0.99954 0.99955 0.999989
Table 5. Reliability evaluation of the model system
2) Reliability evaluation of the Model system
Fig. 15 Reliability-based optimal #2 HVDC association candidates
17
3) Reliability change when adding #3 HVDC
It was assessed through system simulation based on #3 HVDC
construction. Reliability evaluation was conducted based on the
bus of the simulated scenario. Table 6 shows the reliability indices
for each model.
Bus #1 Bus #2 Bus #3 Bus #9 Bus #10 Bus #11
LOLE
[Hrs/year]0.010996 0.011004 0.010996 0.0105 0.010669 0.002811
EENS
[MWh/year]6.29677 6.30115 6.29677 6.086 6.12603 1.58159
EIR
[PU]0.999999 0.999999 0.999999 0.999999 0.999999 1
Table 6. Reliability evaluation result
18
In all cases, it can be estimated that bus 11 is most advantageous. However, in this case,
there is a difficulty in constructing the #3 HVDC because it is required to traverse the
existing #1 HVDC. Therefore, it is considered that #3 HVDC is reasonably superior to bus
10.
Fig. 16 Reliability-based optimal #3 HVDC association candidates
HVDC transmission system between mainland and the Jeju Island
19
⑩⑪
①
#1 HVDC
#2 HVDC
#3 HVDC
Jindo Haenam
Wando
Construction planning
20
As HVDC facilities in power systems has increased, the importance of
reliability evaluation considering this has increased.
Thus, this study proposed a method for establishing HVDC expansion plans
from the perspective of reliability using ComRel of a reliability evaluation
program in HLII developed by a simple method.
This study considered not only forced outage rates (FOR) of generators,
transmission lines, and HVDC but also the uncertainty of WTG with large
variability of output.
It is considered possible to apply this to the establishment of HVDC
expansion plans considering system connections of renewable energy
sources.
CONCLUSION
21
1. Chan-Ki Kim, Vijay K. Sood, Gil-Soo Jang, Seong-Joo Lim and Seok-Jin Lee, “HVDC Transmission: Power Conversion Applications
in Power Systems”, Wily-IEEE Press, Apr. 2009. (ISBN 978-0-0470-82295-1)
2. D. A. Waterworth, C. P. Arnold and N. R. Watson, “Reliability assessment technique for HVdc systems”, IPENZ Transactions,
Vol.25, No.1, Nov. 1998.
3. Wenyuan Li, “Expected Energy Not Served (EENS) Study for Vancouver Island Transmission Reinforcement Project”, Report-BCTC,
Jan. 2006.
4. Osama Swaitti, “Assessing the Impacts of Increasing Penetration of HVDC Lines on Power System Reliability”, KTH Royal Institute
of Technology, May 2007.
5. J. Setreus and L. Bertling, “Introduction to HVDC technology for reliable electrical power systems”, PMAPS 2008, May 2008.
6. ABB Report, “HVDC: technology for energy efficiency and grid reliability”.
7. Les Brand, Ranil de Silva, Errol Bebbington and Kalyan Chilukuri, “Grid West Project HVDC Technology Review”, PSC, Dec. 2014.
8. Kyeonghee Cho, Jeongje Park and Jaeseok Choi, “Probabilistic Reliability Based Grid Expansion Planning of Power System
Including Wind Turbine Generators”, Journal of Electrical Engineering & Technology, Vol.7, No.5, pp.698~704, 2012.
9. Jaeseok Choi, Trungtinh Tran, , A. (Rahim) A. El- Keib, Robert Thomas, HyungSeon Oh and R. Billinton, “A Method for
Transmission System Expansion Planning Considering Probabilistic Reliability Criteria”, IEEE Trans. on Power System, Vol.20, No.3,
pp.1606~1615, Aug. 2005.
10. Jaeseok Choi, “Power System Reliability Evaluation Engineering”, G&U Press, 2013.
11. Jaeseok Choi, Jintaek Lim and Kwang Y. Lee, “DSM Considered Probabilistic Reliability Evaluation and an Information System for
Power Systems Including Wind Turbine Generators”, IEEE Trans. on Smart Grid, Vol.4, No.1, pp.425~432, Mar. 2013.
12. Jaeseok Choi, “Power System Expansion Planning under New Environment”, Green Press, 2016.
13. Kyeonghee Cho, Jaeseok Choi, “Web based Online Real-time Reliability Integrated Information System in Composite Power
System Considering Wind Turbine Generators”, KIEE, Vol.60, No.7, pp.1305~1313, Jul. 2011.
References
22
Appendix(Outage Probability Analysis of
HVDC Converter Considering Spare
Elements)
23
RELIABILITY EVALUATION MODEL FOR HVDC SYSTEM As shown in Figure, a typical HVDC converter consists of a series/parallel
and mixed system.
In Figure 1, 2, 3, 4, 5 and 6, respectively, refer to AC Switchyard, AC Filters,
Capacitor Banks, Converter Transformers, Thyristor Valves, Smoothing
Reactors, DC Filters, and DC Switchyard.
<Structure of Typical HVDC Converter system>
24
For reference, Figure shows a 6-pulse
diode converter bridge of a current
type HVDC converter. This is the
basic structure for understanding the
operation of the HVDC converter.
<6-pulse diode converter>
If the spare factor is “S” and the minimum number of components the
system operates “K”, the total number of components “N” in the system is
formalized as shown in Equation (1).
(1)
25
K out of N system The HVDC transformers will have spare parts in case of failure of the
configuration facilities such as the thyristor and transformers to enhance
their operational reliability. In this paper, the present method for
calculating the probability of systematic failure rate (=unavailability)
considering these component margins was redefined and these status
space sequences were formalized.
In a system consisting of N components, if the system is capable of
performing its functions with more than K components, this is called the
"K out of N" system.
(2)
26
System with a Single Spare A system with “n” identical components and single space can be represented
using four states designated as 0, 1, 2 and 3, with each state defined as follows:
- State 0: System operation, replacement available
- State 1: System outage, replacement available
- State 2: System operation, no replacement available
- State 3: System outage, no replacement available.
A schematic representation of the above conditions is shown in figure, with each
variable defined as follows.
- n : the total number of components in the system
- λ : Outage rate of each component
- R : Replacement time of parts, spare available
- r : Component repair time
27
A-Matrix for 1 Spare
Under steady-state conditions, the probability of a state is obtained using the
above determinant as in Equations.
Therefore, the reliability index of the
system is obtained as shown in Equations.
𝑈𝑠 = 𝑃1 + 𝑃3
𝑓𝑠 = 𝑃1/𝑅
𝑟𝑠 = 𝑅(1 +𝑃3
𝑃1)
𝜆𝑠 = 𝑛𝜆
𝑃0 =1
𝐷
𝑃1 = 𝑛𝜆𝑟 𝑛𝜆 +1
𝑟𝑅 𝑃0
𝐻𝑒𝑟𝑒, 𝐷 = 1 + 𝑛𝜆𝑟 𝑛𝜆 +1
𝑟𝑅 + 𝑛𝜆𝑟 + (𝑛𝜆𝑟)2/2
𝑃2 = (𝑛𝜆𝑟)𝑃0
𝑃3 =𝑛𝜆𝑟 2
2𝑃0
28
System with Two Spares A state transition diagram for a system with an identical element and
two spare elements.
The solution can be expressed in matrix notation as in equation.
Where,P : column vector of state probabilitiesA : coefficient matrix of the 6 equations being usedC : column vector of constants of the 6 equations
At this time, the value of the data parameter is known, the reliability
index value of the system can be calculated using by equations.
𝑈𝑠 = 𝑃1 + 𝑃3 + 𝑃5
𝑓𝑠 = (𝑃1 + 𝑃3)/𝑅
𝑟𝑠 = 𝑅[1 +𝑃5
𝑃1 + 𝑃3]
𝜆𝑠 = 𝑛𝜆
29
<Transition diagram for system with a single spare>
<Transition diagram for system with two spares>
30
Reliability Calculation Flow Chart The reliability of the system is then calculated. Figure shows a flow chart
of reliability calculations.
<Reliability Calculation Flow Chart of HVDC System>
31
CASE STUDY In this study, the methodology for calculating the failure rate considering
spare elements of the HVDC system is presented and, compare and analyze
the case of spares elements.
Parameter Input
n 6
λ 0.012[/year]
R 48[hours]
r 6[months]
<Input Data>
<System with a single Spare>
Parameter Single spare system
Us 0.00102[/year]
fs 0.072[/year]
rs 0.0142[years]
λ 0.072[/year]
<System with two Spares>
Parameter Single spare system
Us 0.000401[/year]
fs 0.072[/year]
rs 0.0056[years]
λ 0.072[/year]
32
1. Variation of System Outage (=un-
availability) according to change of re-
placement time (R)
0
0.0005
0.001
0.0015
0.002
0.0025
0.003 0.006 0.009 0.012 0.015 0.018
Sys
tem
FO
R [
/yea
r]
λ [/year]
R=72 hours
R=48 hours
R=24 hours
R=12 hoursR=06 hours
<single spare system>
2. Variation of System Outage (=un-
availability) according to change of
repair time (r)
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.003 0.006 0.009 0.012 0.015 0.018
Syst
em
F
OR
[/y
ear]
λ [/year]
r = 9 months
r = 6 months
r = 3 months
<single spare system>
In the case of the reliability of the system
decreases as the replacement time of the system
increases.
As shown in Figure, the effect of repair time (r) on
system reliability rather than replacement time (R)
was significant.
Single Spare
33
R=72 hours
R=48 hours
R=24 hours
R=12 hours
R=06 hours
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.001
0.003 0.006 0.009 0.012 0.015 0.018
Sys
tem
FO
R [
/yea
r]
λ [/year]
<Two spares system>
r = 9 months
r = 6 months
r = 3 months
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.003 0.006 0.009 0.012 0.015 0.018
Syst
em
F
OR
[/y
ear]
λ [/year]
<Two spares system>
It can be seen that the reliability of the system is
improved as the spare element is present and the
replacementtimeisreduced.
As shown in Figure, the repair time (r) has little
influence on the system as compared with the
system with a single spare system. This is
probably because of two spares.
Two Spares1. Variation of System Outage (=un-
availability) according to change of re-
placement time (R)
2. Variation of System Outage (=un-
availability) according to change of
repair time (r)
34
Conclusions In this paper, the suggested method for calculating the systematic system
outage (=unavailability) considering the number of spares of the HVDC
system is redefined and formulated as a state space matrix.
We propose an algorithm to estimate the system outage with a single
spare and two spare systems and to perform a sensitivity analysis on the
system reliability by using HDCSR program (HVDC Converter Station
Reliability Program) were newly developed.
In addition, we will apply this to the actual system and analyze the
economic feasibility according to the number of spare elements.
35
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