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Integrating Reliability Models and Adaptive Algorithms for Wind Power Forecasting
CHAPTER 4
Integrating Reliability Models and Adaptive Algorithms for Wind Power Forecasting F. De Caro*, A. Vaccaro*, D. Villacci* *
Department of Engineering, University of Sannio, Benevento, Italy
Abstract The high proliferation of wind generators used in modern electrical grids determines several critical issues pushing power system operators to improve critical operation functions, such as security analysis and spinning reserve assessment, by taking into account the effects of intermittent and nonprogrammable power profiles. To address this challenging issue, a large number of frameworks for wind power forecasting have been proposed in the literature. Although these tools reliably allow prediction of wind speed and theoretical generated power, more complex phenomena need to be investigated to comprehensively model wind power uncertainty and its effect on power system operation. To address this issue, this chapter proposes a probabilistic model based on Markov chains, which predicts the injected power profiles considering wind speed forecasting uncertainty and generator operation states. Experimental results obtained on a real case study are presented and discussed to assess the performance of the proposed method. Keywords: Markov chain, Wind speed forecasting, ECMWF, SCADA, Model fusion, Transition matrix
1 INTRODUCTION The decarbonization process passes through renewable energies deployment, and wind power stands as one of the most efficient technologies. Unfortunately, due to the high proliferation of wind generators in modern electrical grids, the complexity in the control, protection, and prediction of power system operation now grows as a result of several technical and economical side-effects, which are mainly caused by nonprogrammable and intermittent wind generation profiles [1].
Advances in System Reliability Engineering https://doi.org/10.1016/B978-0-12-815906-4.00004-X
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In the current scenario, the role of wind power forecasting tools has been well explored in the literature, outlining their importance in supporting both energy producers and power system operators in mitigating the effects of wind uncertainty, reducing imbalance charges, and obtaining strategic information in day-ahead and real-time energy market trading [2, 3]. Several methodologies, based on both physical and statistical models, have been proposed in the literature for wind power forecasting. Many of them exhibit adaptive features to properly describe wind dynamics, dealing with the intrinsic time-varying phenomena affecting them, and are characterized by low computational resources to satisfy the time constraints of energy management systems [2]. Although the integration of these tools in several power system operation functions allows the enhancement of their performance, primarily by reducing the effects of wind data uncertainty, more complex phenomena need to be investigated to reliably predict real wind generation profiles, assessing the effect of predicted weather variables on the generator operation state. In the light of this need, modern research trends are oriented toward the conceptualization of more sophisticated methods that describe wind generators as stochastic multistate systems, where the state probabilities model the levels of available wind energy [4–6]. In this context the application of the Markov chains has been revealed as one of the most promising research direction [7], and has been adopted in assessing wind generators reliability indices [8]. The main idea is to estimate the effects of the wind speed profiles on the generators’ operational states, which can be roughly determined as “in service” or “faulted.” This process requires the discretization of the wind speed in a certain number of classes and the classification of the generator states for each speed class. Unfortunately, in this kind of approach, the granularity level adopted in discretizing the state variables affects the model accuracy and its complexity. Hence, the identification of a proper level of discretization is an open problem requiring further investigation. To deal with this problem, several approaches have been developed. Wu et al. [9] have proposed a linear rounding method for reducing the number of operational states on the basis of the states’ sequence concept, whereas on the basis of the same concept, a probabilistic model for wind farm modeling in a time-based reliability analysis has been proposed [10]. These approaches are useful for assessing several strategic reliability indices such as the Loss of Energy Expectation and Loss of Load Expectation.
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The described models have been improved by Jiang et al. [11], who describe the effects of the derated working points by using a Monte Carlo method. In accordance with previous, the adoption of a Markov chain base has been only restricted to effectively address the planning problems, whereas their integration in power system operation frameworks are still in the embryonic state and need further investigation. In this context a very promising research approach deals with the fusion of information coming from wind forecasting tools for reliable power profiles assessment for each available wind generator. To address the described problem, this chapter proposes the integration of an adaptive wind forecasting model, which has been proposed by Vaccaro et al. [12], and a probabilistic reliability model based on Markov chains, whose parameters are continuously adjoined by processing real-time operation data. The objective is to compute the wind speed forecasting for the next day on each generator, compute the corresponding forecasting error bounds, and asses the system state probabilities in the function of each wind speed span, by solving a probabilistic multistate system. The described process allows a power system operator to estimate, for each hour of the next day, the expected generated power considering the cumulative effect of all the generation operational states (i.e., alarm, fault, derating operation) and the forecasting errors.
2 PROPOSED METHOD The objective of this chapter is to predict the produced power and generator operation state over time, for both the next day and for each wind generator. To this aim, the fusion of a hybrid forecasting algorithm, which fuses and processes the statistical and physical models’ outputs, and of an adaptable reliability model that is continuously adjoined by real-time operation data, has been developed. The main idea is based on the estimation of the probability density function of wind forecasting error, computing the wind speed tolerance bound, followed by the estimation of the corresponding probability to find the generator in a defined operation state. This is obtained by scientifically by solving a reliability model. Hence, the proposed framework’s main features will be described in the next sections.
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2.1 Wind Speed Forecasting The wind forecasting model applied here has been deployed by Vaccaro et al. [12], in which the prediction supplied by synoptic and local forecasting models are amalgamated by a supervised learning system. In that work the considered synoptic model is a primitive equation for the atmospheric general circulation model, which has been developed by the European Center for Medium-range Weather Forecasts (ECMWF) [13]. Several physical interactions between each of these systems, such as ocean, atmosphere, soil wetness, and snow covering, are covered in that work. Hence, the synoptic model output is corrected by employing an adaptive learning algorithm to improve the forecast accuracy of the wind speed by processing experimental data. The adaptive feature means the opportunity to update the model allows us to consider the effects of “new” operating conditions. In light of the produced results by several case studies, the effectiveness of this forecasting algorithm has been confirmed, proving its adoption in the proposed work.
2.2 Generator Reliability Model In this section, the following generator operation states have been defined to model generator reliability: 1. Alarm: operation in the presence of anomalous working conditions. 2. Faulted: operation inhibited due to a failure condition. 3. Derated: operation in the presence of an external reduction of generated power. 4. Run: normal operation. The wind speed, which is one of the most influential variables ruling the generation state transitions, is classified in the following classes: 1. w < w1 2. w1 w < w2 3. w2 w < w3 4. w w3 where w1, w2, and w3 are the cut-in, rated, and cut-off speeds, respectively. Hence, the state transition diagram in Fig. 1 allows us to describe the generator reliability. The computation of the operation data stored in the Supervisory Control And Data Acquisition (SCADA) event register allows us to determine the
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Fig. 1 Markov model states diagram, preliminary study.
model parameters. Data are organized in a double-column matrix Rz, whose dimensions are [M(z), 2], with z ∈ [1, Nwg], where m ∈ [1, M(z)]. For each row of this matrix correspond the mth transition to a new state: the two columns mean the transition between two different states’ recorded time and the corresponding arrival state codes, respectively. Hence, for each measurement set of Sz, a label has been assigned with a code number by employing Algorithm 1. Then, by adopting Algorithm 2, a square matrix MATz is obtained, which contains for each element the number of transitions from the state ith to jth one.
Algorithm 1 Labeling: ∀z ∈ [1, Nwg]
Algorithm 2 Transitions Counting: ∀z ∈ [1, Nwg]
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Where the number of total states is N. Matrix MATz allows us to compute the transition probabilities as follows: PðjjiÞ ¼
MATz ði, jÞ N X MATz ði, jÞ
(1)
j¼1
Then, the generation state probabilities can be computed at each time class t by iterating the following set of linear equations: pt ¼ pt1 P
(2)
The latter equation allows us to calculate the steady-state probabilities x as follows: 8 x1 ðP11 1Þ + x2 P12 + ⋯ + xN P1N ¼ 0 > > < x1 P21 + x2 ðP21 1Þ + ⋯ + xN P2N ¼ 0 (3) ⋯ ¼0 > > : x1 + x2 + ⋯ + xN ¼1 Or in a matrix-based formalism, as: ∗
xP ¼ b
(4)
where I and P* are the identity and the modified transition matrix, respectively.
2.3 Model Fusion Wind forecasting and generator reliability models have been combined with the purpose of predicting the generated power for each turbine, considering the corresponding expected operation states. Then, to calculate the state probabilities, the formula of total probability, which considers the estimation of the probability density function of the wind speed forecasting error, has been applied: Pðxz Þ ¼
N X PðxðtÞkz jwk ðtÞ wz ðtÞ wk + 1 Þ k¼1
Pðwk wz ðtÞ + eðwz ðtÞÞ wk + 1 Þ
(5)
In this equation, x(t)k represents the probability at time t that zth wind generator is in a fault or alarm state, whereas the true wind speed value wkz ðtÞ
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is included in the kth cluster (wk and wk+1) at the same time. N is the total number of classes, and P(wk wz(t) + e(t) wk+1) is the corresponding probability that the forecasted wind value wz(t), which is affected by the forecasting error e, is included in the k class at the same time.
3 CASE STUDY The proposed method has been applied in the task of estimating the effect of wind forecasting error on the generators’ operation states, considering also the derating states, which are related to the congestion level of the network. For this case study, which is composed of 19 wind generators with 2 MVA rated power, the derating conditions are dictated by the Transmission System Operator to mitigate the effects of power systems’ congestion induced by large wind energy generation. The generator model shown in Fig. 1 and characterized by the transition matrix reported in Table 1 has been deployed. The transition probabilities have been calculated for each wind generator by processing 1 year of firstand second-level SCADA data, with 10 minutes of sampling time. Applying the equation system in Eq. (2) on the latter calculated transition matrix, the following steady-state probabilities have been computed (Table 2) for each wind generator. Their summarization is shown in Fig. 2, with particular reference to the turbine number 3. As shown by the previous results, the estimated average value of derated operational state probability is about the 5% in a 1-year time-window. Unfortunately the described system is not still able to supply information related to the effect of the wind speed on the described generator operation states. Hence, to estimate how the wind speed influences the probability of power curtailments, the Markov model in Fig. 3 has been employed
Table 1 WTG 3: Transition matrix To ( j) From ( j)
Alarm
Derated
Faulted
Run
Alarm Derated Faulted Run
0.9091 0.0003 0.0043 0.0008
0.0021 0.0971 0.0043 0.0019
0.0021 0.0009 0.8369 0.0006
0.0867 0.0274 0.1545 0.9966
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Table 2 Steady-state probabilities WTG Alarm Derated
Faulted
Run
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
0.0137 0.0043 0.0044 0.0035 0.0064 0.0028 0.0065 0.0000 0.0000 0.0000 0.0055 0.0063 0.0069 0.0031 0.0026 0.0077 0.0013 0.0014 0.0013
0.9136 0.9188 0.9253 0.9181 0.9249 0.9145 0.9259 0.5563 0.9951 0.9937 0.9157 0.9125 0.9190 0.9372 0.9283 0.9159 0.9390 0.9306 0.9287
Prob. [–]
Alarm
0.0139 0.0105 0.0090 0.0162 0.0091 0.0186 0.0152 0.4436 0.0048 0.0062 0.0189 0.0189 0.0175 0.0099 0.0199 0.0199 0.0126 0.0149 0.0197
Alarm regime
0.0586 0.0663 0.0611 0.0621 0.0595 0.0640 0.0522 0.0000 0.0000 0.0000 0.0598 0.0622 0.0566 0.0496 0.0491 0.0564 0.0470 0.0529 0.0501
Derated
Derated regime
Faulted regime
0 5
10
15
20 25 30 Time (1 u = 10 min) Run
Prob. [–]
Faulted
0.05
35
40
45
50
35
40
45
50
Run regime
1 0.95 5
10
15
20
25
30
Time (1 u = 10 min)
Fig. 2 Markov’s transient probability evolution.
considering the wind speed clusters in Table 3. Algorithm 1 allows us to calculate the following Transition Matrix, which is reported in Table 4. The computed transition matrix is indispensable to calculate the generators’ operation probabilities by applying Eq. (2), whose results are shown in
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Fig. 3 Considered Markov model states diagram.
Table 3 Bins codes
Alarm Derated Faulted Run
w
w >w1 w
w >w2 w
w >w3
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
Table 2. Unfortunately this analysis reveals lack of homogeneity with reference to the considered number of wind speed classes. In fact, a further subdivision of wind speed cluster in greater class numbers allows us to estimate the probabilistic profile of the wind effect on the generator operation state (Table 5). Hence, to quantify this effect, Eq. (5) has been employed allowing the estimation of the derating generated power profiles for each turbine, which are summarized in Fig. 4. It is remarkable how the wind turbines show different levels of derated generated power in a period of 1 year that the different derating probabilities derive. This should suggest curtailment sequence policies in the function of potential wind resource availability. Then, as a natural consequence of the described data analysis, the conclusive study of this chapter is the statistical assessment on the impact level of wind
1 2 3 4 Derated 5 6 7 8 Faulted 9 10 11 12 Run 13 14 15 16
From Alarm (i)
0.8038 0.0461 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009 0.0001 0.0000 0.0000
1
0.0696 0.8582 0.1212 0.0000 0.0000 0.0005 0.0000 0.0000 0.0000 0.0083 0.0000 0.0000 0.0000 0.0008 0.0000 0.0000
2
0.0000 0.0142 0.8788 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3
Alarm
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4
0.0000 0.0000 0.0000 0.0000 0.7967 0.0049 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0003 0.0000 0.0000
5
Table 4 Transition matrix with wind speed clusters: WTG 3
0.0000 0.0035 0.0000 0.0000 0.0488 0.9043 0.1149 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0020 0.0048 0.0000
6
0.0000 0.0000 0.0000 0.0000 0.0000 0.0584 0.8778 0.0000 0.0000 0.0000 0.0164 0.0000 0.0000 0.0000 0.0133 0.0000
7
Derated
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
8
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.6600 0.0744 0.0000 0.0000 0.0004 0.0000 0.0000 0.0000
9
To ( j)
0.0000 0.0035 0.0000 0.0000 0.0000 0.0010 0.0000 0.0000 0.2000 0.7107 0.0492 0.0000 0.0001 0.0006 0.0000 0.0000
10
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009 0.0000 0.0000 0.0248 0.8197 1.000 0.0000 0.0000 0.0072 0.0000
11
Faulted
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0012 0.0000
12
0.1013 0.0035 0.0000 0.0000 0.0732 0.0025 0.0000 0.0000 0.1400 0.0083 0.0000 0.0000 0.9026 0.0569 0.0000 0.0000
13
0.0253 0.0709 0.0000 0.0000 0.0813 0.0265 0.0000 0.0000 0.0000 0.1736 0.0000 0.0000 0.0957 0.9342 0.1812 0.0000
14
0.0000 0.0000 0.0000 0.0000 0.0000 0.0020 0.0055 0.0000 0.0000 0.0000 0.1148 0.0000 0.0000 0.0051 0.7899 0.5000
15
Run
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0024 0.5000
16
0.0091 0.0051 0.0054 0.0058 0.0049 0.0075 0.0073 0.1510 0.0011 0.0017 0.0058 0.0061 0.0036 0.0028 0.0042 0.0036 0.0031 0.0049 0.0048
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
0.0029 0.0039 0.0030 0.0098 0.0037 0.0103 0.0068 0.2751 0.0038 0.0046 0.0129 0.0124 0.0137 0.0071 0.0157 0.0164 0.0096 0.0084 0.0141
2
WTG 1
0.0019 0.0015 0.0006 0.0007 0.0005 0.0008 0.0011 0.0177 0.0000 0.0000 0.0002 0.0005 0.0003 0.0001 0.0000 0.0000 0.0000 0.0016 0.0008
3
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4
0.0016 0.0025 0.0023 0.0217 0.0036 0.0054 0.0015 0.0000 0.0000 0.0000 0.0026 0.0051 0.0050 0.0048 0.0051 0.0072 0.0083 0.0051 0.0050
5
0.0277 0.0333 0.0383 0.0276 0.0392 0.0270 0.0264 0.0000 0.0000 0.0000 0.0283 0.0302 0.0283 0.0216 0.0252 0.0306 0.0321 0.0256 0.0234
6
0.0294 0.0304 0.0203 0.0127 0.0166 0.0314 0.0242 0.0000 0.0000 0.0000 0.0288 0.0267 0.0231 0.0230 0.0186 0.0184 0.0066 0.0225 0.0216
7
Table 5 Steady-state probabilities with wind speed clusters Alarm Derated
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
8
0.0019 0.0016 0.0010 0.0016 0.0019 0.0005 0.0024 0.0000 0.0000 0.0000 0.0029 0.0017 0.0016 0.0005 0.0015 0.0058 0.0006 0.0005 0.0004
9
0.0105 0.0002 0.0023 0.0017 0.0032 0.0019 0.0026 0.0000 0.0000 0.0000 0.0022 0.0037 0.0037 0.0017 0.0006 0.0016 0.0003 0.0008 0.0007
10
0.0012 0.0007 0.0012 0.0002 0.0013 0.0004 0.0013 0.0000 0.0000 0.0000 0.0003 0.0010 0.0016 0.0010 0.0004 0.0002 0.0004 0.0001 0.0002
11
Faulted
0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
12
0.2527 0.3342 0.3403 0.4039 0.3603 0.3995 0.3463 0.2029 0.6732 0.4596 0.3781 0.4111 0.4551 0.4855 0.4691 0.4977 0.5514 0.3936 0.4438
13
0.6284 0.5613 0.5694 0.4920 0.5496 0.4925 0.5452 0.3192 0.2758 0.4797 0.5105 0.4739 0.4452 0.4278 0.4332 0.4002 0.3763 0.5017 0.4629
14
0.0321 0.0232 0.0157 0.0225 0.0151 0.0227 0.0344 0.0340 0.0458 0.0540 0.0271 0.0275 0.0187 0.0238 0.0262 0.0181 0.0115 0.0351 0.0223
15
Run
0.0005 0.0002 0.0001 0.0001 0.0001 0.0000 0.0002 0.0001 0.0003 0.0004 0.0002 0.0002 0.0002 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000
16
n
<
w
<
* 39 0.
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
w 9* .3
0
wn
n
<
w
<
*w
48 0.
Fig. 4 Derating probability.
0
w 0* .3
Steady-state derating probability [–]
*w
48 0.
n
n
<
w
< *w
57 0.
n *w 57 . 0 n
<
<
0
*w
5 .6
n
<
w
<
7 0.
4* *w 4 .7 0
wn
n
<
w
<
< n *w
3 .8 0
wn 3* 8 0.
Wind speed intervals [–] wn = 11.5 m/s
w
wn
5*
6 0.
w
<
9 0.
1*
wn
0.
< n *w 1 9
w
<
wn < n *w
w
<
08 2.
WTG19
WTG18
WTG17
WTG16
WTG15
WTG14
WTG13
WTG12
WTG11
WTG10
WTG9
WTG8
WTG7
WTG6
WTG5
WTG4
WTG3
WTG2
WTG1
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Speed [–]
2
1
0 0
5
10
15
20
25
30
35
40
45
50
30
35
40
45
50
Mean hourly prob. [–]
Time (h)
0.015 0.01 0.005 0 0
5
10
15
20
25
Time (h)
Fig. 5 WTG 3 derating forecasting on next 48 hours.
forecasting uncertainty on wind generator derating power probabilities by calculating them for each turbine. To estimate the time evolution of wind forecasting errors, the application of Eq. (5) becomes crucial. The deviation of the expected profile from the real one allows us to quantify the effect of the actual wind speed figure on the generation operation, as shown in Fig. 5. Thus this analysis reveals it is not worth claiming the relevant effect of the wind forecasting uncertainty in the perturbation of generator operation estimation profiles. In fact the induced deviations on the estimated profile could determine conservative curtailments by the system operator to prevent a risk of possible network congestion. Moreover, it is evident that there is a proportional correlation between the wind speed magnitude and the derating probabilities, namely the increase of wind speed corresponds with a rise of curtailment risks.
4 CONCLUSION The massive proliferation of wind generators in modern power systems pushes the system operator to equip themselves with advanced forecasting tools for the optimal management of the generator assets, dealing with the crucial issue of mitigating data uncertainties effects. To face this issue, this chapter proposes a forecasting framework aimed at both predicting wind power profiles and the effects of weather variables on the generator operation state. A probabilistic model, based on Markov chains, has been adopted
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to predict the reduced generated power profiles to prevent congestion on the network, considering the effects of wind speed forecasting uncertainty and the expected generator operation state. To prove the effectiveness of the proposed method, several case studies have been presented, and the most relevant results have been analyzed.
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Integrating Reliability Models and Adaptive Algorithms for Wind Power Forecasting F. De Caro*, A. Vaccaro*, D. Villacci* *
Department of Engineering, University of Sannio, Benevento, Italy
Abstract The high proliferation of wind generators used in modern electrical grids determines several critical issues pushing power system operators to improve critical operation functions, such as security analysis and spinning reserve assessment, by taking into account the effects of intermittent and nonprogrammable power profiles. To address this challenging issue, a large number of frameworks for wind power forecasting have been proposed in the literature. Although these tools reliably allow prediction of wind speed and theoretical generated power, more complex phenomena need to be investigated to comprehensively model wind power uncertainty and its effect on power system operation. To address this issue, this chapter proposes a probabilistic model based on Markov chains, which predicts the injected power profiles considering wind speed forecasting uncertainty and generator operation states. Experimental results obtained on a real case study are presented and discussed to assess the performance of the proposed method. Keywords: Markov chain, Wind speed forecasting, ECMWF, SCADA, Model fusion, Transition matrix
1 INTRODUCTION The decarbonization process passes through renewable energies deployment, and wind power stands as one of the most efficient technologies. Unfortunately, due to the high proliferation of wind generators in modern electrical grids, the complexity in the control, protection, and prediction of power system operation now grows as a result of several technical and economical side-effects, which are mainly caused by nonprogrammable and intermittent wind generation profiles [1].
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In the current scenario, the role of wind power forecasting tools has been well explored in the literature, outlining their importance in supporting both energy producers and power system operators in mitigating the effects of wind uncertainty, reducing imbalance charges, and obtaining strategic information in day-ahead and real-time energy market trading [2, 3]. Several methodologies, based on both physical and statistical models, have been proposed in the literature for wind power forecasting. Many of them exhibit adaptive features to properly describe wind dynamics, dealing with the intrinsic time-varying phenomena affecting them, and are characterized by low computational resources to satisfy the time constraints of energy management systems [2]. Although the integration of these tools in several power system operation functions allows the enhancement of their performance, primarily by reducing the effects of wind data uncertainty, more complex phenomena need to be investigated to reliably predict real wind generation profiles, assessing the effect of predicted weather variables on the generator operation state. In the light of this need, modern research trends are oriented toward the conceptualization of more sophisticated methods that describe wind generators as stochastic multistate systems, where the state probabilities model the levels of available wind energy [4–6]. In this context the application of the Markov chains has been revealed as one of the most promising research direction [7], and has been adopted in assessing wind generators reliability indices [8]. The main idea is to estimate the effects of the wind speed profiles on the generators’ operational states, which can be roughly determined as “in service” or “faulted.” This process requires the discretization of the wind speed in a certain number of classes and the classification of the generator states for each speed class. Unfortunately, in this kind of approach, the granularity level adopted in discretizing the state variables affects the model accuracy and its complexity. Hence, the identification of a proper level of discretization is an open problem requiring further investigation. To deal with this problem, several approaches have been developed. Wu et al. [9] have proposed a linear rounding method for reducing the number of operational states on the basis of the states’ sequence concept, whereas on the basis of the same concept, a probabilistic model for wind farm modeling in a time-based reliability analysis has been proposed [10]. These approaches are useful for assessing several strategic reliability indices such as the Loss of Energy Expectation and Loss of Load Expectation.
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The described models have been improved by Jiang et al. [11], who describe the effects of the derated working points by using a Monte Carlo method. In accordance with previous, the adoption of a Markov chain base has been only restricted to effectively address the planning problems, whereas their integration in power system operation frameworks are still in the embryonic state and need further investigation. In this context a very promising research approach deals with the fusion of information coming from wind forecasting tools for reliable power profiles assessment for each available wind generator. To address the described problem, this chapter proposes the integration of an adaptive wind forecasting model, which has been proposed by Vaccaro et al. [12], and a probabilistic reliability model based on Markov chains, whose parameters are continuously adjoined by processing real-time operation data. The objective is to compute the wind speed forecasting for the next day on each generator, compute the corresponding forecasting error bounds, and asses the system state probabilities in the function of each wind speed span, by solving a probabilistic multistate system. The described process allows a power system operator to estimate, for each hour of the next day, the expected generated power considering the cumulative effect of all the generation operational states (i.e., alarm, fault, derating operation) and the forecasting errors.
2 PROPOSED METHOD The objective of this chapter is to predict the produced power and generator operation state over time, for both the next day and for each wind generator. To this aim, the fusion of a hybrid forecasting algorithm, which fuses and processes the statistical and physical models’ outputs, and of an adaptable reliability model that is continuously adjoined by real-time operation data, has been developed. The main idea is based on the estimation of the probability density function of wind forecasting error, computing the wind speed tolerance bound, followed by the estimation of the corresponding probability to find the generator in a defined operation state. This is obtained by scientifically by solving a reliability model. Hence, the proposed framework’s main features will be described in the next sections.
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2.1 Wind Speed Forecasting The wind forecasting model applied here has been deployed by Vaccaro et al. [12], in which the prediction supplied by synoptic and local forecasting models are amalgamated by a supervised learning system. In that work the considered synoptic model is a primitive equation for the atmospheric general circulation model, which has been developed by the European Center for Medium-range Weather Forecasts (ECMWF) [13]. Several physical interactions between each of these systems, such as ocean, atmosphere, soil wetness, and snow covering, are covered in that work. Hence, the synoptic model output is corrected by employing an adaptive learning algorithm to improve the forecast accuracy of the wind speed by processing experimental data. The adaptive feature means the opportunity to update the model allows us to consider the effects of “new” operating conditions. In light of the produced results by several case studies, the effectiveness of this forecasting algorithm has been confirmed, proving its adoption in the proposed work.
2.2 Generator Reliability Model In this section, the following generator operation states have been defined to model generator reliability: 1. Alarm: operation in the presence of anomalous working conditions. 2. Faulted: operation inhibited due to a failure condition. 3. Derated: operation in the presence of an external reduction of generated power. 4. Run: normal operation. The wind speed, which is one of the most influential variables ruling the generation state transitions, is classified in the following classes: 1. w < w1 2. w1 w < w2 3. w2 w < w3 4. w w3 where w1, w2, and w3 are the cut-in, rated, and cut-off speeds, respectively. Hence, the state transition diagram in Fig. 1 allows us to describe the generator reliability. The computation of the operation data stored in the Supervisory Control And Data Acquisition (SCADA) event register allows us to determine the
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Fig. 1 Markov model states diagram, preliminary study.
model parameters. Data are organized in a double-column matrix Rz, whose dimensions are [M(z), 2], with z ∈ [1, Nwg], where m ∈ [1, M(z)]. For each row of this matrix correspond the mth transition to a new state: the two columns mean the transition between two different states’ recorded time and the corresponding arrival state codes, respectively. Hence, for each measurement set of Sz, a label has been assigned with a code number by employing Algorithm 1. Then, by adopting Algorithm 2, a square matrix MATz is obtained, which contains for each element the number of transitions from the state ith to jth one.
Algorithm 1 Labeling: ∀z ∈ [1, Nwg]
Algorithm 2 Transitions Counting: ∀z ∈ [1, Nwg]
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Where the number of total states is N. Matrix MATz allows us to compute the transition probabilities as follows: PðjjiÞ ¼
MATz ði, jÞ N X MATz ði, jÞ
(1)
j¼1
Then, the generation state probabilities can be computed at each time class t by iterating the following set of linear equations: pt ¼ pt1 P
(2)
The latter equation allows us to calculate the steady-state probabilities x as follows: 8 x1 ðP11 1Þ + x2 P12 + ⋯ + xN P1N ¼ 0 > > < x1 P21 + x2 ðP21 1Þ + ⋯ + xN P2N ¼ 0 (3) ⋯ ¼0 > > : x1 + x2 + ⋯ + xN ¼1 Or in a matrix-based formalism, as: ∗
xP ¼ b
(4)
where I and P* are the identity and the modified transition matrix, respectively.
2.3 Model Fusion Wind forecasting and generator reliability models have been combined with the purpose of predicting the generated power for each turbine, considering the corresponding expected operation states. Then, to calculate the state probabilities, the formula of total probability, which considers the estimation of the probability density function of the wind speed forecasting error, has been applied: Pðxz Þ ¼
N X PðxðtÞkz jwk ðtÞ wz ðtÞ wk + 1 Þ k¼1
Pðwk wz ðtÞ + eðwz ðtÞÞ wk + 1 Þ
(5)
In this equation, x(t)k represents the probability at time t that zth wind generator is in a fault or alarm state, whereas the true wind speed value wkz ðtÞ
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is included in the kth cluster (wk and wk+1) at the same time. N is the total number of classes, and P(wk wz(t) + e(t) wk+1) is the corresponding probability that the forecasted wind value wz(t), which is affected by the forecasting error e, is included in the k class at the same time.
3 CASE STUDY The proposed method has been applied in the task of estimating the effect of wind forecasting error on the generators’ operation states, considering also the derating states, which are related to the congestion level of the network. For this case study, which is composed of 19 wind generators with 2 MVA rated power, the derating conditions are dictated by the Transmission System Operator to mitigate the effects of power systems’ congestion induced by large wind energy generation. The generator model shown in Fig. 1 and characterized by the transition matrix reported in Table 1 has been deployed. The transition probabilities have been calculated for each wind generator by processing 1 year of firstand second-level SCADA data, with 10 minutes of sampling time. Applying the equation system in Eq. (2) on the latter calculated transition matrix, the following steady-state probabilities have been computed (Table 2) for each wind generator. Their summarization is shown in Fig. 2, with particular reference to the turbine number 3. As shown by the previous results, the estimated average value of derated operational state probability is about the 5% in a 1-year time-window. Unfortunately the described system is not still able to supply information related to the effect of the wind speed on the described generator operation states. Hence, to estimate how the wind speed influences the probability of power curtailments, the Markov model in Fig. 3 has been employed
Table 1 WTG 3: Transition matrix To ( j) From ( j)
Alarm
Derated
Faulted
Run
Alarm Derated Faulted Run
0.9091 0.0003 0.0043 0.0008
0.0021 0.0971 0.0043 0.0019
0.0021 0.0009 0.8369 0.0006
0.0867 0.0274 0.1545 0.9966
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Table 2 Steady-state probabilities WTG Alarm Derated
Faulted
Run
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
0.0137 0.0043 0.0044 0.0035 0.0064 0.0028 0.0065 0.0000 0.0000 0.0000 0.0055 0.0063 0.0069 0.0031 0.0026 0.0077 0.0013 0.0014 0.0013
0.9136 0.9188 0.9253 0.9181 0.9249 0.9145 0.9259 0.5563 0.9951 0.9937 0.9157 0.9125 0.9190 0.9372 0.9283 0.9159 0.9390 0.9306 0.9287
Prob. [–]
Alarm
0.0139 0.0105 0.0090 0.0162 0.0091 0.0186 0.0152 0.4436 0.0048 0.0062 0.0189 0.0189 0.0175 0.0099 0.0199 0.0199 0.0126 0.0149 0.0197
Alarm regime
0.0586 0.0663 0.0611 0.0621 0.0595 0.0640 0.0522 0.0000 0.0000 0.0000 0.0598 0.0622 0.0566 0.0496 0.0491 0.0564 0.0470 0.0529 0.0501
Derated
Derated regime
Faulted regime
0 5
10
15
20 25 30 Time (1 u = 10 min) Run
Prob. [–]
Faulted
0.05
35
40
45
50
35
40
45
50
Run regime
1 0.95 5
10
15
20
25
30
Time (1 u = 10 min)
Fig. 2 Markov’s transient probability evolution.
considering the wind speed clusters in Table 3. Algorithm 1 allows us to calculate the following Transition Matrix, which is reported in Table 4. The computed transition matrix is indispensable to calculate the generators’ operation probabilities by applying Eq. (2), whose results are shown in
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Fig. 3 Considered Markov model states diagram.
Table 3 Bins codes
Alarm Derated Faulted Run
w
w >w1 w
w >w2 w
w >w3
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
Table 2. Unfortunately this analysis reveals lack of homogeneity with reference to the considered number of wind speed classes. In fact, a further subdivision of wind speed cluster in greater class numbers allows us to estimate the probabilistic profile of the wind effect on the generator operation state (Table 5). Hence, to quantify this effect, Eq. (5) has been employed allowing the estimation of the derating generated power profiles for each turbine, which are summarized in Fig. 4. It is remarkable how the wind turbines show different levels of derated generated power in a period of 1 year that the different derating probabilities derive. This should suggest curtailment sequence policies in the function of potential wind resource availability. Then, as a natural consequence of the described data analysis, the conclusive study of this chapter is the statistical assessment on the impact level of wind
1 2 3 4 Derated 5 6 7 8 Faulted 9 10 11 12 Run 13 14 15 16
From Alarm (i)
0.8038 0.0461 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009 0.0001 0.0000 0.0000
1
0.0696 0.8582 0.1212 0.0000 0.0000 0.0005 0.0000 0.0000 0.0000 0.0083 0.0000 0.0000 0.0000 0.0008 0.0000 0.0000
2
0.0000 0.0142 0.8788 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
3
Alarm
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4
0.0000 0.0000 0.0000 0.0000 0.7967 0.0049 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0003 0.0000 0.0000
5
Table 4 Transition matrix with wind speed clusters: WTG 3
0.0000 0.0035 0.0000 0.0000 0.0488 0.9043 0.1149 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0020 0.0048 0.0000
6
0.0000 0.0000 0.0000 0.0000 0.0000 0.0584 0.8778 0.0000 0.0000 0.0000 0.0164 0.0000 0.0000 0.0000 0.0133 0.0000
7
Derated
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
8
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.6600 0.0744 0.0000 0.0000 0.0004 0.0000 0.0000 0.0000
9
To ( j)
0.0000 0.0035 0.0000 0.0000 0.0000 0.0010 0.0000 0.0000 0.2000 0.7107 0.0492 0.0000 0.0001 0.0006 0.0000 0.0000
10
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009 0.0000 0.0000 0.0248 0.8197 1.000 0.0000 0.0000 0.0072 0.0000
11
Faulted
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0012 0.0000
12
0.1013 0.0035 0.0000 0.0000 0.0732 0.0025 0.0000 0.0000 0.1400 0.0083 0.0000 0.0000 0.9026 0.0569 0.0000 0.0000
13
0.0253 0.0709 0.0000 0.0000 0.0813 0.0265 0.0000 0.0000 0.0000 0.1736 0.0000 0.0000 0.0957 0.9342 0.1812 0.0000
14
0.0000 0.0000 0.0000 0.0000 0.0000 0.0020 0.0055 0.0000 0.0000 0.0000 0.1148 0.0000 0.0000 0.0051 0.7899 0.5000
15
Run
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0024 0.5000
16
0.0091 0.0051 0.0054 0.0058 0.0049 0.0075 0.0073 0.1510 0.0011 0.0017 0.0058 0.0061 0.0036 0.0028 0.0042 0.0036 0.0031 0.0049 0.0048
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
0.0029 0.0039 0.0030 0.0098 0.0037 0.0103 0.0068 0.2751 0.0038 0.0046 0.0129 0.0124 0.0137 0.0071 0.0157 0.0164 0.0096 0.0084 0.0141
2
WTG 1
0.0019 0.0015 0.0006 0.0007 0.0005 0.0008 0.0011 0.0177 0.0000 0.0000 0.0002 0.0005 0.0003 0.0001 0.0000 0.0000 0.0000 0.0016 0.0008
3
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
4
0.0016 0.0025 0.0023 0.0217 0.0036 0.0054 0.0015 0.0000 0.0000 0.0000 0.0026 0.0051 0.0050 0.0048 0.0051 0.0072 0.0083 0.0051 0.0050
5
0.0277 0.0333 0.0383 0.0276 0.0392 0.0270 0.0264 0.0000 0.0000 0.0000 0.0283 0.0302 0.0283 0.0216 0.0252 0.0306 0.0321 0.0256 0.0234
6
0.0294 0.0304 0.0203 0.0127 0.0166 0.0314 0.0242 0.0000 0.0000 0.0000 0.0288 0.0267 0.0231 0.0230 0.0186 0.0184 0.0066 0.0225 0.0216
7
Table 5 Steady-state probabilities with wind speed clusters Alarm Derated
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
8
0.0019 0.0016 0.0010 0.0016 0.0019 0.0005 0.0024 0.0000 0.0000 0.0000 0.0029 0.0017 0.0016 0.0005 0.0015 0.0058 0.0006 0.0005 0.0004
9
0.0105 0.0002 0.0023 0.0017 0.0032 0.0019 0.0026 0.0000 0.0000 0.0000 0.0022 0.0037 0.0037 0.0017 0.0006 0.0016 0.0003 0.0008 0.0007
10
0.0012 0.0007 0.0012 0.0002 0.0013 0.0004 0.0013 0.0000 0.0000 0.0000 0.0003 0.0010 0.0016 0.0010 0.0004 0.0002 0.0004 0.0001 0.0002
11
Faulted
0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
12
0.2527 0.3342 0.3403 0.4039 0.3603 0.3995 0.3463 0.2029 0.6732 0.4596 0.3781 0.4111 0.4551 0.4855 0.4691 0.4977 0.5514 0.3936 0.4438
13
0.6284 0.5613 0.5694 0.4920 0.5496 0.4925 0.5452 0.3192 0.2758 0.4797 0.5105 0.4739 0.4452 0.4278 0.4332 0.4002 0.3763 0.5017 0.4629
14
0.0321 0.0232 0.0157 0.0225 0.0151 0.0227 0.0344 0.0340 0.0458 0.0540 0.0271 0.0275 0.0187 0.0238 0.0262 0.0181 0.0115 0.0351 0.0223
15
Run
0.0005 0.0002 0.0001 0.0001 0.0001 0.0000 0.0002 0.0001 0.0003 0.0004 0.0002 0.0002 0.0002 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000
16
n
<
w
<
* 39 0.
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
w 9* .3
0
wn
n
<
w
<
*w
48 0.
Fig. 4 Derating probability.
0
w 0* .3
Steady-state derating probability [–]
*w
48 0.
n
n
<
w
< *w
57 0.
n *w 57 . 0 n
<
<
0
*w
5 .6
n
<
w
<
7 0.
4* *w 4 .7 0
wn
n
<
w
<
< n *w
3 .8 0
wn 3* 8 0.
Wind speed intervals [–] wn = 11.5 m/s
w
wn
5*
6 0.
w
<
9 0.
1*
wn
0.
< n *w 1 9
w
<
wn < n *w
w
<
08 2.
WTG19
WTG18
WTG17
WTG16
WTG15
WTG14
WTG13
WTG12
WTG11
WTG10
WTG9
WTG8
WTG7
WTG6
WTG5
WTG4
WTG3
WTG2
WTG1
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Speed [–]
2
1
0 0
5
10
15
20
25
30
35
40
45
50
30
35
40
45
50
Mean hourly prob. [–]
Time (h)
0.015 0.01 0.005 0 0
5
10
15
20
25
Time (h)
Fig. 5 WTG 3 derating forecasting on next 48 hours.
forecasting uncertainty on wind generator derating power probabilities by calculating them for each turbine. To estimate the time evolution of wind forecasting errors, the application of Eq. (5) becomes crucial. The deviation of the expected profile from the real one allows us to quantify the effect of the actual wind speed figure on the generation operation, as shown in Fig. 5. Thus this analysis reveals it is not worth claiming the relevant effect of the wind forecasting uncertainty in the perturbation of generator operation estimation profiles. In fact the induced deviations on the estimated profile could determine conservative curtailments by the system operator to prevent a risk of possible network congestion. Moreover, it is evident that there is a proportional correlation between the wind speed magnitude and the derating probabilities, namely the increase of wind speed corresponds with a rise of curtailment risks.
4 CONCLUSION The massive proliferation of wind generators in modern power systems pushes the system operator to equip themselves with advanced forecasting tools for the optimal management of the generator assets, dealing with the crucial issue of mitigating data uncertainties effects. To face this issue, this chapter proposes a forecasting framework aimed at both predicting wind power profiles and the effects of weather variables on the generator operation state. A probabilistic model, based on Markov chains, has been adopted
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to predict the reduced generated power profiles to prevent congestion on the network, considering the effects of wind speed forecasting uncertainty and the expected generator operation state. To prove the effectiveness of the proposed method, several case studies have been presented, and the most relevant results have been analyzed.
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