274 Journal of International Council on Electrical Engineering Vol. 1, No. 3, pp. 274~280, 2011
Probabilistic Reliability Evaluation of Composite Power Systems Including Wind Turbine Generators Kyeonghee Cho *, Jeongje Park *, Taegon Oh *, Jaeseok Choi †, Seongeun Hong ** and Mohammad Shahidehpour *** Abstract – This paper proposes a new methodology for evaluating the probabilistic reliability of a grid constrained composite power system including wind turbine generators(WTG). The proposed model can consider capacity limitations and transmission line forced outage rates. The importance of renewable energy sources has been growing at a high rate as a result of being environment friendly. In particular, wind energy is one of the most successfully utilized such source to produce electrical energy. The random nature of wind speed can be incorporated in the evaluation by representing the WTG by multi state models. A simple case study shows in detail how it is used to perform a reliability evaluation study in proposed model. Keywords: Wind turbine generator, Grid considered reliability evaluation, Multi-state model, Composite power system reliability evaluation
1. Introduction As a result of being environmental friendly, the utilization of renewable resources such as the wind and the sun to generate electric power has received considerable attention in recent years [1], [2]. Wind energy in particular has been fast growing and is recognized as the most successful energy source of all the available sources. The location of wind turbine generators(WTG) depends on the available wind speed conditions. Therefore, grid constrained reliability evaluation is very important for grid expansion planning and operation when WTGs are added in a power system. Composite power system reliability evaluation and probabilistic production simulation modeling is complex and WTG cannot be adequately represented by simple two state models. Two-state models for WTG create large errors in accuracy and multi-state models should be used. Relevant wind speed models have been combined with WTG characteristics to create multistate model of WTG. The research has been carried out to evaluate reliability of generation systems(HLI) that include WTGs by using multi-state model of WTG[2-5]. Corresponding Author: Dept. of Electrical Engineering, ERI, Gyeongsang National University, Jinju, GN, Korea (
[email protected]) * Dept. of Electrical Engineering, ERI, Gyeongsang National University, Jinju, GN, Korea (
[email protected],
[email protected],
[email protected]) ** A vice-chief, KEPCO, Busan, Korea (
[email protected]) *** Dept. of Electrical and Computer Engineering, IIT, USA, (
[email protected]) Received: May 9, 2011; Accepted: June 14, 2011
Composite power systems that include WTGs also require multi-state WTG models in addition to considering grid uncertainty associated with lines, main transformers and switch gear etc. As huge WTGs penetration is expected in the near future, the development of methodology for the WTG’s multi-state model considered reliability evaluation considering uncertainty of grid becomes essential even if it is a difficult and complicated task. In this paper, a new methodology for grid constrained probabilistic reliability evaluation of power systems including WTG is proposed. A composite power system reliability evaluation methodology based on the composite power system effective load model has been developed by the authors [6], [7]. This methodology used two-state models of both generators and transmission lines. This paper extends the two-state representation to multi-state models for generators in order to consider WTG. A composite power system reliability model, CMELDC[7], is used for considering grid uncertain associated with lines, main transformers and switch gears etc.[6], [7]. This paper describes the effectiveness of the proposed method through the case studies.
†
2. The Multi-state Operation Model of WTG 2.1 WTG Power Output Model Fig. 1 shows the relationship between the power output of a WTG and the wind speed [1]-[5].
Kyeonghee Cho, Jeongje Park, Taegon Oh, Jaeseok Choi, Seongeun Hong and Mohammad Shahidehpour Power output [MW]
275
2.3 The Multi-state Model of WTG
The power output model of a WTG combined with the wind speed model shown in Fig. 3 yields the multi-state model. Each state has a pair of associated parameters; namely the power (Pi) and probability (PBi). The operation model of a WTG is in the form of a multi-state model described by an outage capacity probability distribution function.
PR
VR
Vci
Vco
Wind Velocity
Fig. 1. A typical power output model of WTG. Power[MW ]
Where, Vci: the cut-in speed [m/sec]. VR: the rated speed [m/sec]. Vco: the cut-out speed [m/sec]. PR: the rated power [MW].
( Pn , PBn )
( Pi + 2 , PBi + 2 ) ( Pi +1 , PBi +1 ) ( Pi , PBi )
A mathematical model for the power output of a WTG is given as (1) [2]. The power, Pi generated by wind speed band SWi can be formulated as (1) [2]. Where, i is the wind speed. The A, B, and C parameters equations are given in the Appendix.
wind Velocity
pdf
μ − 5σ μ − 4σ μ − 3σ
μ − 2σ
μ −σ
μ
μ +σ
μ + 2σ μ + 3σ
μ + 4σ
μ + 5σ
wind Velocity
Pi = 0, 0 ≤ SWi < Vci = PR ( A + B × SWi + C × SWi 2 ), Vci ≤ SWi < VR
(1)
= PR , VR ≤ SWi ≤ Vco = 0, Vco < SWi
Fig. 3. Development of a model describing the power outputs of WTG and the corresponding probabilities.
3. Reliability Evaluation of A Composite Power System including WTG
2.2 Wind speed model
Wind speeds vary both in time and space. It is has been reported that the actual wind speed distribution can be described by a Weibull probability distribution and approximated by a normal distribution[2]. This paper 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. 2. The negative wind speed value in Fig. 2 has no physical meaning and can be ignored. pdf
Composite power system reliability evaluation methodologies based on both enumeration methods and Monte Carlo methods have been developed[9-12]. A composite power system reliability evaluation methodology based on the composite power system effective load model has also been developed by the authors [7]. This methodology used two-state models to describe the generators and transmission lines. This paper extends the two-state generations unit representation to multi-state models in order to consider WTG. 3.1 Reliability Evaluation at HLI including WTG
μ − 5σ μ − 4σ μ − 3σ μ − 2σ
μ −σ
μ
μ +σ
μ + 2σ μ + 3σ μ + 4σ μ + 5σ
Wind Velocity
Fig. 2. Wind speed model.
Reliability indices of LOLEHLI (Loss of load expectation) and EENSHLI(Expected energy not served) at HLI considering only the generation system are calculated using the effective load duration curve(ELDC), HLIΦ(x) as in (2) and (3) respectively.
Probabilistic Reliability Evaluation of Composite Power Systems Including Wind Turbine Generators
276
LOLE HLI = HLI Φ ( x ) EENS HLI = ∫
IC + Lp
IC
HLI
x = IC
Φ ( x )dx
[hours/yr]
(2)
[MWh/yr]
(3)
k
Φ i ( xe ) = k Φ o ( xe ) ⊗k f osi ( xoi ) = ∫ k Φ o ( xe − xoi ) k f osi ( xoi )dxoi
(7)
where, ⊗: the operator representing the convolution integral kΦ0 = original load duration curve at load point #k kfosi: outage capacity pdf of the synthesized fictitious generator created by generators 1 to i, at load point #k.
where, IC : total installed generating capacity [MW] Lp : system peak load [MW] And, HLI
Φi ( xe ) = HLI Φi −1 ( xe ) ⊗HLI f oi ( xoi ) = ∫ HLI Φi −1 ( xe − xoi ) HLI f oi ( xoi )dx
(4) CT1 , qt1 CT2 , qt 2
where, ⊗: operator meaning convolution intergral HLI Φ0(xe - xoi)= HLIΦ(xL ) HLIfoi(xoi): the probability distribution function of outage capacity of generator #i
CTi , qti
(a) Actual system
EENSk = ∫
APk + Lp k
APk
k
[hours/yr]
(5)
Φ NG ( x )dx [MWh/yr]
(6)
x = APk
where, Lpk : peak load at load point k[MW] APk : maximum arrival power at load point k[MW]
k k
xL
k
APi1 q i1
k k
xL
APi 2 qi 2
k
k k
xL
k
APij q ij
k k
xL
APiNS q iNS
∑
k
f osi ( x oj )
k
AP sij
q sij k
k
xL
(b) Synthesized fictitious equivalent generator
CT2 , qt 2 = 0
The load point reliability indices, LOLEk and EENSk can be calculated using (5) and (6) with the CMELDC, kΦNG(x).
LOLE k = k Φ NG ( x )
k
CT1 , qt1 = 0
1) Reliability indices at the load points(buses)
xL
CTNT , qtNT
3.2 Reliability Evaluation at HLII (Composite Power System) including WTG
The reliability indices at HLII can be classified as load point indices and bulk system indices depending on the object of the evaluation. The reliability indices can be evaluated using a Composite power system Equivalent Load Duration Curve (CMELDC) based on the composite power system effective load model in Fig.4 [6], [7]. CG, CT and go and ql in Fig. 4 are the capacities and outage capacity distribution functions of the generators and the forced outage rates of the transmission lines respectively. The model uses the outage capacity distribution functions of the generators in order to consider the WTG as multi-state generators. The transmission line state model remained as a two-state representation.
k
k
CTi , qti = 0 CTNT , qtNT = 0
xL ⎧ APNGj
k
xoNGj ⎪⎨ k
⎪⎩ k qNGj
(c) Equivalent system Fig. 4. Composite power system effective load model at HLII.
The outage capacity pdf of the synthesized fictitious generator created by generators 1 to i, at load point #k (kfosi) is also a multi-state function. The convolution integral between the original load duration curve at load point #k (kΦ0) and kfosi is processed at HLII. The general multi-state
Kyeonghee Cho, Jeongje Park, Taegon Oh, Jaeseok Choi, Seongeun Hong and Mohammad Shahidehpour
277
convolution integral calculation method for probabilistic reliability evaluation has been used extensively for generation expansion and can be calculated using the multistate recursive equation shown in (8). kΦi
= k Φ i -1 ⊗ kf osi NS
NS
n =1
n =1
= (1 - ∑ kq ni ) k Φ i -1 ( x ) + ∑ kq ni k Φ i -1 ( x - kC ni )
(8)
where, Φ0: the original Inverted Load Duration Curve (ILDC) x: random variable of Φ NS: the multi-state number of the synthesized fictitious generator kCni: outage capacity of state n of the synthesized fictitious generator created by generator at load point #k. q : k ni the probability correspond the outage capacity of state k of the synthesized fictitious generator at load point #k. kfosi: outage capacity pdf of the synthesized fictitious generator at load point #k. 2) Reliability indices of the bulk system While the EENSHLII of a bulk system is equal to the summation of the EENSk at the load points as shown in (9), 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 (10), an equivalent defined LOLEHLII of the bulk system can be calculated using (11). NL
EENS HLII = ∑ EENS k
[MWh/yr]
Fig. 5. The step-by-step process for evaluating the reliability of a power system involving WTGs.
3. Case study The proposed method was applied to the 8-bus model system as shown in Fig. 6. Table 1 shows the system data with Generators, Transmission Lines and Loads representing the generators, transmission lines and loads respectively. SB(Start Bus) and EB(End Bus) are the start and end buses of the line respectively.
(9)
k =1
NL
ELC HLII = ∑ ELC k
[MW/cur.yr]
(10)
k =1
LOLEHLII = EENSHLII / ELCHLII [hours/yr] EIRK = 1− EENS K / DENGK
[PU]
(11) (12)
where, NL : number of load points ELCk = EENSk/ LOLEk DENGk : demand enegy at bus #k
Fig. 6. 8-bus model system.
Fig. 5 shows a flow chart of the proposed method to evaluate the reliability of a composite power system including WTGs.
Probabilistic Reliability Evaluation of Composite Power Systems Including Wind Turbine Generators
278
Table 1. System data with generators(GEN), transmission lines(TRL) and loads(LOD)
1 0.9 0.8
SB 0 0 0 0 0 0 0 0 0 1 1 2 3 3 4 5 2 4 4 7 8 2 3 4 5 7 6
EB 1 8 1 8 1 8 2 2 2 2 3 4 4 5 5 6 8 7 6 6 7 9 9 9 9 9 9
ID WTG GEN GEN GEN GEN GEN GEN GEN GEN TRL TRL TRL TRL TRL TRL TRL TRL TRL TRL TRL TRL LOD LOD LOD LOD LOD LOD
Capacity[MW] 20 40 20 20 10 10 40 20 5 50 90 90 50 50 50 40 50 50 50 50 90 20 65 40 40 85 40
FOR 0.03 0.025 0.025 0.02 0.02 0.02 0.015 0.01 0.004568 0.001713 0.00571 0.001142 0.001142 0.001142 0.00571 0.004568 0.001142 0.001142 0.001142 0.001713 -
The wind turbine generator was assumed in generation system of the model system. The available capacity probability distribution function(ACPDF) considering 5state model for the wind generator is shown in Fig. 7. Fig. 8 shows the inverted load duration curves(ILDC) at the load buses.
0.7 0.6
Load [pu]
NL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
bus 2
0.5
bus 3
0.4
bus 4
0.3
bus 5
0.2
bus 7
0.1
bus 6
0 1
2 3
4
5
6 7
8
bus 7 9 10 11 bus 4 12 13 14 15 16 bus 2 17 18 19 20 21 22 23 24 hours
Fig. 8. Inverted load duration curves at system buses.
Table 2 shows the calculated LOLE, EENS and EIR reliability indices for the buses and the system respectively. In this case, base case, the capacity of WTG is 20MW. Table 3 shows the results when the capacity of WTG is 40MW (case 1). The reliability was better than before the capacity of WTG increased at all buses and system. Table 4 shows the reliability indices of model system when the system considered transmission system or not. The reliability of base case was worse than the case that did not considered grid (case 2). Table 2. Reliability indices at buses and system(base case)
Num
Load Bus#
LOLE [hrs/yr]
EENS [MWh/yr]
EIR [MW/cur.yr]
1
2
13.2903
28.7774
0.999811
2
3
26.7272
88.7484
0.999825
3
4
7.26644
20.6087
0.999931
4
5
7.26644
20.6087
0.999931
5
6
29.3669
116.865
0.999924
6
7
7.26644
20.6087
0.999931
16.4805
296.217
0.999867
System
Table 3. Reliability indices at buses and system(case 1)
Num
Fig. 7. ACPDF of wind generator (5-state model).
1 2 3 4 5 6 System
Load Bus#
LOLE [hrs/yr]
EENS [MWh/yr]
EIR [MW/cur.yr]
2 3 4 5 6 7
11.0969 23.1845 6.12303 6.12303 25.1296 6.12303 14.0518
23.9908 76.2189 17.3470 17.3470 99.2535 17.3470 251.504
0.999842 0.999850 0.999942 0.999942 0.999851 0.999942 0.999887
Kyeonghee Cho, Jeongje Park, Taegon Oh, Jaeseok Choi, Seongeun Hong and Mohammad Shahidehpour
Table 4. Reliability indices of model system
LOLE [hours/day] EENS [MWh/day] EIR [pu]
Grid not constrained Case (case 2)
Grid constrained Case (base case)
11.2536
16.4805
200.427
296.217
0.999910
0.999867
[3]
[4]
[5]
4. Conclusion This paper presents a new methodology for grid constrained probabilistic reliability evaluation of power systems including wind turbine generators using the composite power system effective load model developed by authors[7]. The generator multi-state modeled composite power system effective load is utilized in order to consider WTGs. The previous model used two-state models for generators and transmission lines. The proposed model utilizes a multi-state model of a generator to consider WTG, obtained by combining the wind speed model and the WTG’s power output model. The proposed method is demonstrated by a case study which is the 8-bus system. The reliability level of grid constrained case is lower than it of grid not constrained case. The difference between them depends on the capacity and forced outage rate of grid. The proposed method provides useful information about the quantitative contribution or location determination of WTG in viewpoint of composite power system reliability and grid expansion planning under large WTG penetration.
[6]
[7]
[8]
[9]
[10]
Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0000156). The support of the Advanced Power Network Reliability Research Center (APRRC) is acknowledged.
References [1] Nick Jenkins, Ron Allan, Peter Crossley, David Kirschen, Goran Strbac, Embedded Generation, 2000, pp. 31-38 [2] Rajesh Karki, Po Hu, Roy Billinton, “A Simplified
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Wind Power Generation Model for Reliability Evaluation,” IEEE Transactions on Energy Conversion, Vol. 21, No. 2, June 2006 Singh, Lago-Gonzalez, “Reliability Modeling of Generation Systems Including Unconventional Energy Sources,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, No.5, May 1985 Billinton, R., Gan, L, “Wind Power Modeling and Application in Generating Adequacy Assessment,” Proceedings, the 14th Power Systems Computation Conference, Sevilla, Spain, June 24-28, 2000 Liang Wu, Jeongje Park, Jaeseok Choi, A. A. El-Keib, Mohammad Shahidehpour, and Roy Billinton, “Probabilistic Reliability Evaluation of Power Systems Including Wind Turbine Generators Using a Simplified Multi-State Model: A Case Study” IEEE, PES, GM2009, July 26-30, Calgary, 2009 Jaeseok Choi, Hongsik Kim, Junmin Cha and Roy Billinton; "Nodal Probabilistic Congestion and Reliability Evaluation of a Transmission System under Deregulated Electricity Market", proc. of conference, Vancouver, Canada, IEEE, PES, SM2001, July 16-19, 2001 J. Choi, R. Billinton and M. Futuhi-Firuzabed “Development of a New Nodal Effective Load Model Considering Transmission System Element Unavailabilities” to be published by IEE proceedings on GTD, 2005 Boy Billinton, Wenyuan Li, Reliability Assessment of Electric Power Systems Using Monte Carlo Methods, 1994, pp. 24-30 Roy Billinton and Wenyuan Li, Reliability Assessment of Electric Power Systems Using Monte Carlo Methods, Plenum Press, 1994 Roy Billinton and Ronald N. Allan, Reliability Evaluation of Power Systems, Second Edition, Plenum Press, 1996 Jaeseok Choi, Timothy Mount, Robert Thomas and Roy Billinton, "Probabilistic Reliability Criterion for Planning Transmission System Expansions" IEE G,T&D, Vol.153, No.6, pp.719-727, November, 2006
Kyeonghee Cho was born in Jinhea, Korea in 1987. She received the B.Sc degrees from Gyeongsang National Univercity, Jinju, in 2010. Her research interest includes reliability evaluation of power systems considering renewable energy. He is now working forward a M.Sc. degree at Gyeongsang National University.
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Probabilistic Reliability Evaluation of Composite Power Systems Including Wind Turbine Generators
Jeongje Park (S’08) was born in Jinju, Korea in 1981. He received the B.Sc. and M.Sc. degrees from Gyeongsang National University, Jinju, in 2007 and 2008, respectively. His research interest includes probabilistic reliability evaluation of power systems including renewable resources. He is now working forward a Ph.D. degree at Gyeongsang National University.
Taegon Oh was born in Jinju, Korea in 1984. His research interest includes Transmission Expansion Planning using Reliability Evaluation of Power Systems. He received the B.Sc. degree from Gyeonsang National University, Jinju, in 2010. He is now working forward a M.Sc. degree at Gyeongsang National University.
Jaeseok Choi (S’88–M’91–SM’05) was born in Kyeongju, Korea, in 1958. He received the B.Sc., M.Sc., and Ph.D. degrees from Korea University, Seoul, in 1981, 1984, and 1990, respectively. He was a Postdoctoral at the University of Saskatchewan, Saskatoon, SK, Canada, in 1996. He was a visiting professor at Cornell University, Ithaca, NY, USA, in 2004. Since 1991, he has been on the faculty of Gyeongsang National University, Jinju, Korea, where he is a professor. He is also adjunct professor at IIT, IL, USA since 2007. His research interests include fuzzy applications, probabilistic production cost simulation, reliability evaluation, and outage cost assessment of power systems.
Mohammad Shahidehpour (F’01) is the Carl Bodine Distinguished Professorand Chairman in the Electrical and Computer Engineering Department at theIllinois Institute of Technology, Chicago.Dr. Shahidehpour is an IEEE Distinguished Lecturer and has lectured in 30 countries on electricity restructuring issues. He is the Vice President of Publications for IEEE/PES.
