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Reliability Assessment of Wind Power System Considering
Multi-objective Models
ChunHong ZHAO 1,a, LianGuang LIU 1,b, ZiFa LIU 1,c, Ying Chen1,d 1School of Electrical and Electronic Engineering, North China Electric Power University, Beijing
102206, China
Keywords: wind farms; multi-objective models; risk indicators; the non-sequential Monte Carlo simulation
Abstract. The integration of wind farms has a significant impact on the power system reliability. An
appropriate model used to assess wind power system reliability is needed. Establishing
multi-objective models (wind speed model, wind turbine generator output model and wind farm
equivalent model) and based on the non-sequential Monte Carlo simulation method to calculate risk
indicators is a viable method for quantitatively assessing the reliability of power system including
wind farms. The IEEE-RTS 79 test system and a 300MW wind farm are taken as example.The
calculation resluts show that using the multi-objective models can improve accuracy and reduce error;
the higher average wind speed obtains the better system reliabitity accordingly.
Introduction
The intermittent and randomness of wind power has a significant impact on the reliable operation of
the power grid [1]. Reliability assessment is a key problem for the planning and operation of the
power systems containing wind farms.In the previous calculation, a wind farm is equivalent to a wind
turbine generator (WTG) generally.Such a treatment produces small error for the small-scale wind
farms, but large error for the large-scale wind farms [2]. Modeling each WTG is difficult to achieve
because of the large amount of calculation.
Muljadi and Butteerfied [3] used a detailed model considering each WTG model.This method is
accurate, but its simulation scale is large and time is long. Hua and Li [4,5,6] treated wind farm as an
equivalent generator to study generation and transmission system reliability including wind farms.In
this paper, risk indicators are calculated establishing multi-objective models (wind speed model,
WTG output model and wind farm equivalent model) of wind farm, based on the non-sequential
Monte Carlo simulation method. Taking the IEEE-RTS 79 test system and a 300MW wind farm as
example, risk index is calculated and wind power system reliability is evaluated quantitatively.
Evaluation Model of Wind Farm
Model of Wind Speed. Time-series models can be used to analyze wind speed sequence [7].In this
paper, the ARMA model is uitilized. Firstly, the original wind speed sequence { (0)
tv } need to be
standardized.The new sequence { tv } is calculated as:
(0)
tt
ν
ν
ν µν
σ−
= . (1)
where νµ and 2
νσ is respectively the mean and variance of original sequence { (0)
tv }.
The ARMA (p,q) model is established as:
1 1 2 2 1 1t t t n t n t t m t ma a aν ϕν ϕ ν ϕ ν θ θ− − − − −= + + ⋅⋅⋅ + + − − ⋅⋅⋅ − . (2)
where ( 1,2, , )i i nϕ = ⋅⋅⋅ is autoregressive parameter; ( 1, 2, , )j j mθ = ⋅⋅⋅ is moving average
parameter;{ }ta is residuals, 2(0, )ta N ασ∈ .
Advanced Materials Research Vols. 608-609 (2013) pp 742-747Online available since 2012/Dec/13 at www.scientific.net© (2013) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMR.608-609.742
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 130.207.50.37, Georgia Tech Library, Atlanta, USA-16/11/14,14:03:40)
Model of WTG Output. The output of WTG depends on wind characteristics. A WTG output lies
between zero and the rated value because of constant variations in the wind input.
The WTG power output can be calculated as:
0 ( ) ( )
(v)=
ci co
ciR ci R
R ci
R R
v v v v
v vP P v v v
v v
P v v
≤ ≥ −
≤ ≤−
≥
∪
. (3)
where RP is rated power output; civ , Rv and cov is respectively cut-in wind speed, rated wind speed
and cut-out wind speed.
Equivalent Model of Wind Farm. Assuming the wind speed of wind farm is the same, wind farm
can be treated as one wind turbine integrated into the grid [8],as shown in Fig.1.However, the wind
speed in different locations is different considering the practical terrain factors and wake effects.So
wind generators can be divided to a number of fleet followed the location of installation and unit
type.That is a wind farm is equivalent to multi-wind turbines, then each wind turbine drives the same
capacity induction generator, as shown in Fig.2.
Outage Model of WTG. The outage of WTG is modeled by means of a two-state Markov process
[9,10] in the paper. The transitions between the operative and failed states are characterized by the
failure rate λ and repair rate µ . Generally thinking, normal operating duration 1τ and repair
duration 2τ are all exponential distribution, λ and µ both are Constant. Normal 1τ and 2τ can be
calculated as:
1 1 1
1= ln = lnMTTFτ γ γ
λ− − . (4)
2 2 2
1= ln = lnMTTRτ γ γ
λ− − . (5)
where 1γ and 2γ are random variables of uniform distributions, MTTF is mean time to failure and
MTTR is mean time to repair.
The Reliability Evaluation of Wind Power Systems
The Basic Steps of Assessment.
1) Establish component probability model;
A composite generation and transmission system consists of generators, transformers, buses,
transmission lines, circuit breakers, protective relaying and so on. All system components are
modeled as the two-state Markov model [11] in this paper.
W1
……
……
W2
Wn
The equivalent wind turbine
The
grid
Fig.2. Wind farm is equivalent to
multi-wind turbines
The wind wheel
Fig.1. Wind farm is equivalent to a single
wind turbine
The generator
The transformer
C
The gear box The grid
Advanced Materials Research Vols. 608-609 743
2) Select system state and calculate its probability;
In this paper,the non-sequential Monte Carlo simulation method is used to select system state
[11].The sampling frequency of the system state s can be as unbiased estimate of its probability.It is
written as [12]:
( )( )
n sP s
N= . (6)
where N is the sampling number; n(s) is the occurrence number of the state s.
3) Assess consequence of system failure;
The BPA software is used to calculate the cut load when system is fault.
4) Calculate risk index;
The risk indicators based on the non-sequential Monte Carlo simulation method are written as:
(1) PLC (probability of load curtailments)
s
( )
F
n sPLC
N∈
=∑ . (7)
where F is the set of all failed states under the annual maximum load level.
(2) EENS (expected energy not supplied) （MWh）
s
( )( )
F
n sEENS C s
N∈
=∑ . (8)
where C(s) is load reductions of the states (MW).
(3) EFLC (expected frequency of load curtailments)
( )
1
( )( )
m s
jj
s F
n sEFLC
Nλ
=∈
= ∑∑ . (9)
where jλ is the transfer rate of the component j , m(s) is the total number of transfer rates.
(4) ADLC (average duration of load curtailments) （h）
8760PLCADLC
EFLC
×= . (10)
(5) ELC (Expected Load Curtailments) （MW）
(s)s F
ELC C∈
=∑ . (11)
(6) BPII （Bulk Power Interruption Index）
/BPII ELC L= . (12)
where L is the annual maximum load of system (MW).
(7) BPECI （Bulk Power Energy Curtailment Index） (h)
/BPECI EENS L= . (13)
Model of Load Shedding. In this paper, the optimal load shedding model based on AC power flow is
used [13].Meanwhile, two important principles are considered:
1) Cut the load relatively closer to the bus of failure components priority；
2) Cut load by importance of load, the least important is cut firstly and the most one is cut finally.
744 Progress in Renewable and Sustainable Energy
Case studies
Test System Introduction. The IEEE-RTS 79 test system and a 300MW wind farm are as example in
the paper.The IEEE-RTS 79 test system consists of 32 generating units .The total installed capacity is
3405MW, and the suggested annual peak load is 2850MW.The diagram of the IEEE-RTS 79 is shown
in Fig.3. The outage data and parameters of conventional generators,transformers,lines and other
components in the system are shown in [14]. There are 300 WTGs in the wind farm, every WTG is
same type and install capacity is 1MW.The cut-in,rated and cut-out wind speed are respectively
3m/s,12m/s and 25m/s.The wind speed data is from a wind farm in Hami.
Risk Index Calculation. The 300MW wind farm is integrated in the bus 18. The risk index is
calculated using the optimal load shedding model.
The Risk Index Calculation under Different Equivalent Programs.Assuming there are three
equivalent solutions. They are:
1) G1: the wind farm is equivalent to a single wind turbine, that is the 300 wind turbines are treated
as a generator;
2) G3: the wind farm is equivalent to three wind turbines, that is each adjacent 100 wind turbines
are treated as a generator;
3) G5: the wind farm is equivalent to five wind turbines, that is each adjacent 60 wind turbines are
treated as a generator.
The risk indicators calculation results as given in Table 1.
Bus
1
Bus
2
Bus 3
Bus
4
Bus
5
Bus
6
Bus
7
Bus
8
Bus
9
Bus
10
Bus 11 Bus
12
Bus
24
Bus
13
Bus
15
Bus
14
Bus
16 Bus
19
Bus
20
Bus
17
Bus
18Bus
21 Bus
22
Bus
23
A
B
C
DG
E
F
138 kV
230 kV
Synch.
Cond.
Fig.3. Diagram of the original IEEE-RTS 79
Advanced Materials Research Vols. 608-609 745
Table 1 The risk index calculation results under three equivalent programs
Risk index G1 G3 G5
EENS[MWh] 5529.37 5126.78 5023.54
PLC 0.0104 0.00902 0.00874
EFLC 4.502 4.088 4.065
ELC[MW] 10373.09 9618.11 9424.16
ADLC[h] 20.24 19.33 18.83
BPII 3.64 3.37 3.31
BPECI[h] 1.94 1.79 1.76
As given in Table 1, there are some differences in the risk index results when the wind farm is
equivalent into 1, 3 and 5 wind turbines.The results of G1 and G5 are respectively maximum and
minimum, and the two results vary widely.However, the G3 risk indicators are similar to G5.This
shows that treating a wind farm as multi-wind turbines can make the risk index decline, error reduce
and the calculation results closer the actual reliability of system.
The Risk Index Calculation of Different Wind Speed and Wind Speed Fluctuation.Three
assess solutions are designed considering the equivalent program G5. They are:
1) WS1: the mean wind speed is 6m/s, the wind speed variance is 1.5;
2) WS2: the mean wind speed is 10m/s, the wind speed variance is 1.5;
3) WS3: the mean wind speed is 10m/s, the wind speed variance is 4.
The risk indicators calculation results as given in Table 2.
Table 2 The risk index calculation results of different wind speed and wind speed fluctuation
Risk index WS1 WS2 WS3
EENS[MWh] 4582.36 4369.25 4695.57
PLC 0.00452 0.00343 0.00625
EFLC 3.398 3.231 3.605
ELC[MW] 8596.51 8196.71 8808.89
ADLC[h] 11.65 9.30 15.2
BPII 3.02 2.88 3.09
BPECI[h] 1.61 1.53 1.65
The table 2 indicated that, the test system is more reliable after the wind farm is integrated in the
system.Access solution WS2 is the most obvious.BPII and BPECI decreased by 12.9% and13.1%
respectively.This is because that wind farm is equivalent to new generators, so the power supply
capacity of system is improved.Comparing the results of WS1 and WS2, it can be seen that the
greater average wind speed is, the better system reliablity is.This is due to the fact that output of wind
farm will increase with the increasing of average wind speed.It is shown in the results of WS2 and
WS3 that the increasing of wind speed variance lowers the system reliability slightly.This can be
explained that wind speed variance reflects wind speed fluctuation and increasing of wind speed
fluctuation causes the system reliability to reduce.Meanwhile,from WS1 and WS3,we can know when
average wind speed is improved,the influence of wind speed fluctuation is weakened relatively.
Summary
It is a viable method to calculate risk index using the non-sequential Monte Carlo simulation method
and establishing multi-objective models of wind farm. The risk index declines, error reduces and the
calculation results closer the actual reliability of system when wind farm is treated as multi-wind
turbines.
746 Progress in Renewable and Sustainable Energy
The calculation results show that the average wind speed has a great impact on the wind power
reliability; the greater the average wind speed is, the better the system reliability is.This is because that
the output power of wind farm increases as wind speed increases.The results also show that the
increasing of wind speed variance slightly reduces the wind power system reliability; the wind speed
fluctuations have a small impact on the reliability when the average wind speed increases. The greater
average wind speed and the smaller wind speed fluctuation are, the better the system reliability is.
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Progress in Renewable and Sustainable Energy 10.4028/www.scientific.net/AMR.608-609 Reliability Assessment of Wind Power System Considering Multi-Objective Models 10.4028/www.scientific.net/AMR.608-609.742
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