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On the development of dynamic stroke density for transmission line for power system operational applications
Electrical Power and Energy Systems 116 (2020) 105527
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
On the development of dynamic stroke density for transmission line for power system operational applications
T
⁎
Ernesto Pereza, , Jairo Espinosaa, Daniel Arangurenb a b
Universidad Nacional de Colombia, Departamento de Energía Eléctrica y Automática, Medellín, Colombia Keraunos S.A.S, Colombia
A R T I C LE I N FO
A B S T R A C T
Keywords: Lightning parameters Lightning location systems Tropical regions Lightning density maps Keraunic level Parameter estimation
This paper proposes a method to estimate the impact of lightning activity on transmission lines. The method uses a time-variant density parameter described using kernel basis functions. The algorithm is implemented and tested with historical data in real transmission lines located in Colombia for the years 2015 and 2016. Statistical analysis is performed to observe the lightning activity on each line, characterizing its severity in density magnitude and the duration of it. The correlation of this parameter with the line failures is also analyzed. Finally, the paper concludes that this parameter could be useful for applications on a real-time operation.
1. Introduction Electric power systems are critical infrastructure because the society and economy are dependable of it. Besides, the electric power system is indispensable for other critical systems, such as gas infrastructure, water supply, financial, services, telecommunications, public health, transportation, among others [1]. Lightning is one of the major causes of failure in electric power systems, where, according to several authors, more than 60% of the transmission lines failures are due to this phenomenon [2]. Traditionally, power system infrastructure is protected against lightning through insulation coordination techniques, which may include insulation level enhancement, shielding wires, and surge protective devices [3,4]. This methodology is based mainly on information, voltage rate, environmental conditions, and ground flash density. The lightning information is gathered on a keraunic level or Lightning Location Systems, being more reliable the latter [5]. The traditional design only uses the ground flash density as an average of yearly basis information, neglecting the dynamical behavior of thunderstorms. Nowadays, lightning location systems installed all over the world provide real-time data which create new possibilities for operational uses in different sectors. Two main government bodies had addressed the good practices: The IEC62793 standard [6], which deals with the framework of thunderstorm warning systems and the implementation of preventive hazard measures, and the Federal Aviation Administration (FAA), in the ACRP report eight [7] deals with lightning warning systems focused on airports.
⁎
Recently Tong et al. [8] proposed the concept of Dynamic Lightning Protection (DLP), which is an operational concept where the lightning activity is taken into account to take preventive actions to reduce the possibility of power outages. The warning process used is based on the two area concept, defined in the IEC62793 standard [6]. The two area concept for warning defines two areas: one called area of concern (AOC) containing the infrastructure to be protected, and other called area of warning (AOW), which encloses the AOC. A warning will be triggered once lightning strikes inside the AOW and is turned off if no strikes are detected in the AOW after a given dwell-time. This concept is very useful; however, it may produce a large number of false alarms [9]. The general lightning-related failure risk of power lines is commonly simplified by the assumption of simple collecting area and the calculation of a flash collection rate as given in IEEE 1243 standard ec (1) [10], based on a constant Ground Flash Density obtained from historical multi-annual values.
28h0.6 + b ⎞ Ns = Ng ⎛⎜ ⎟ 10 ⎠ ⎝
(1)
where Ng is the Ground Flash Density Ns is the flashes/100 km/year h is the tower height b is the separation distance between the external ground or phase wires. The approach in this paper considers a real-time calculation of the lightning risk based on a dynamic concept of the lightning (stroke) density. The proposed methodology is intended to provide a dynamic estimation of the impact of lightning activity on transmission lines.
Corresponding author at: Cra 80, No 65-223, M8-205, Facultad de Minas, Medellín, Colombia. E-mail addresses: [email protected] (E. Perez), [email protected] (J. Espinosa), [email protected] (D. Aranguren).
https://doi.org/10.1016/j.ijepes.2019.105527 Received 16 April 2019; Received in revised form 6 July 2019; Accepted 1 September 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
Electrical Power and Energy Systems 116 (2020) 105527
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Furthermore, the paper presents a correlation between the proposed dynamic parameter and line failures. This paper is organized as follows: Section 2 describes and define the concept of dynamic stroke density (DSD). The implementation algorithm is presented in Section 3. Section 4 makes a description of the vulnerability of transmission lines. Statistical analysis for the DSD on real transmission lines is analyzed in Section 5. In Section 6 is presented possible applications for real-time uses in power system operation. Finally, conclusions are presented in Section 7. 2. Transmission line dynamic stroke density We define transmission line DSD as a function in time and lightning activity. First, we estimate the stroke density on the transmission line based on a kernel density estimator [11] which is being implemented by several authors in different applications [12–14]. As a basic concept, we use for each stroke a kernel function K: → that satisfies the condition of Eq. (2).
Fig. 2. Representation of transmission line by means of piece-wise linear segments.
∞
∫−∞ Ki (s) ds = 1
(2) path and will not be a perfect straight segment. In this case, we can represent the line as a linear piece-wise path as shown in Fig. 2. Integrating each straight segment to find the density d as expressed in Eq. (7).
where s is the variable in space. For our case we use a Gaussian kernel given by Eq. (2) s2
K (s ) =
− 1 e 2σs2 σs 2π
(3)
M
d=
where σs is the standard deviation of distance, also known as smoothing parameter, and s is the distance from the stroke. We can establish that the range of influence of a stroke is approximately 3σs . The magnitude of σs must be larger than the lightning location accuracy. The density function for each stroke for a given transmission line, as shown in Fig. 1, can be expressed as (6). The stroke density along the line di varies between 0 and 1 as a function of s.
di =
∫C K (s) dl
⎡Stroke/line⎤ ⎥ ⎢ ⎦ ⎣
∫0
1
K (λ ) dλ
⎡Stroke/line⎤ ⎥ ⎢ ⎦ ⎣
K
⎞ ⎞ ⎛⎛ 1 − λ aj + λbj dλ ⎟ ⎟ ⎜⎜ ⎠ ⎠ ⎝⎝
(7)
where aj and bj are the extremes of the straight segment. For a Gaussian kernel the expression may be written in terms of erf: M
d=
2π σs ⎡ ⎛ 2 ⎛ ⎞⎞ ⎛ 2 s ⎟⎞⎤ erf ⎜ ⎜sa + Δl j ⎟ ⎟ − erf ⎜ aj ⎥ 4Δl j ⎢ ⎝ 2σs ⎝ j ⎠⎠ ⎝ 2σs ⎠⎦ ⎣
∑ j=1
(8)
where Δl j = aj − bj is the straight distance between the points aj and bj , and the erf function is:
(4)
2 π
erf(x ) =
∫0
x
2
e−t dt
(9)
The density described above is static and does not take into account the time evolution of the lightning activity, for this reason, we proposed to multiply the calculated density with a decaying time function as shown in (10).
(5)
Therefore, the density along the path is:
di =
1
j=1
where C is the contour of the function l (λ ) describing the path of the transmission line from the beginning (λ = 0 ) till the end (λ = 1). The function relating s and λ is given by
s (λ )2 = l (0)T l (0) + 2l (0)T l (λ ) + l (λ )T l (λ )
∑ ∫0
di (t ) =
(6)
In real configurations, a transmission line will have an irregular
∫0
1
K (λ ) dλfi (t ) ⎡Stroke/line⎤ ⎥ ⎢ ⎦ ⎣
(10)
where f (t ) be any decreasing function that represents the reducing factor of density in time so that new strokes contribute more on the density than old strokes. In our case we define a exponential function as shown in Eq. (11).
fi (t ) = e−
(t − ti) τ
(11)
where ti is the time of occurrence of the stroke, t is the current time and τ is decay constant. The total density along the line for N strokes on the vicinity of the line will be: N
D (t ) =
∑ i=1
di (t )
(12)
where i denotes each stroke. Since D is a function of distance, time, and the number of strokes, this factor implicitly comprises the evolution of lightning rate and the vicinity of lightning activity. The exponential function of time allows giving more importance to the recent strokes and less significance to old ones.
Fig. 1. Geometrical configuration of lightning strike and straight transmission line. 2
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Fig. 5. Characteristics of the dynamic stroke density D (t ) for a transmission line during a thunderstorm event.
Fig. 3. Lightning activity near a transmission line with an observation time window of 30 min. Yellow dots represent each stroke. Blue line represents a 500 kV transmission line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
one (column 1). The parameters used for the case of analysis are: σs = 10 [km], tw = 30 [min], Δt = 1 [min], Ll = 500 [m]. Once the instantaneous value of the kernel is calculated for the time window and along the length, it must be weighted with the time factor shown in Eq. (11). In order to do so, we will create a vector T ∈ RN with entries:
3. Dynamic stroke density estimation algorithm The proposed concept is implemented to analyze lightning data and real transmission lines. It uses real-time data provided by the lightning location system, as shown in Fig. 3. This procedure has the following steps: The transmission line tower location is read, obtaining M segments of a defined length of Ll . Every Δt , the database is queried for all strokes that occurred in the previous period. Only the strokes within a 4σs distance to the lines are selected for the estimation of the density using (6) for each segment of the line. The information is stored in a matrix A ∈ RM × W for a time window tw , where W = tw /Δt . Therefore the entries of the matrix A (t ) will be computed as:
∑ p=1
⎦
(14)
Finally the density D (t ) for a given line is computed as:
D (t ) = A (t ) T
1
(15)
where . 1 denotes the norm-1 of the vector or the sum of the absolute values of the entries of the vector. Fig. 5 shows the values of the D (t ) 4. Vulnerability
P (t − (j − 1)Δt )
Ai, j (t ) =
−(W − 1)Δt T −Δt ⎤ τ , …, e τ
T = ⎡1, e ⎣
∫a
bi
i
⎛ ⎞ K sp (l) dl ⎜ ⎟ ⎝ ⎠
The failure condition of power transmission lines is finally dependent on the hazard severity, computed as previously described; but also on the system vulnerability given by the insulation level, overvoltage protection elements, grounding values, materials, among many others. Electromagnetic transient analyses would be necessary to understand how a given condition of direct or indirect lightning incidence causes a given failure condition such as a back flashover, shielding failure flashover or other. Such scenarios represent a wide number of possible combinations and situations. The vulnerability can be alternatively understood as the cause-effect relation derived from the dynamic risk behavior, as previously discussed, and the historical performance of the real power transmission system, that is also dynamic. This approach does not allow to keep visible all the details of the electromagnetic phenomenon but leads to understanding useful and more practical patterns of the system performance. Next section goes deeper in the described approach.
(13)
where P (t − (j − 1)Δt ) is the number of strokes in the time window of t − j Δt < t ⩽ t − (j − 1)Δt , ai and bi are the extremes of the i-th line segment, and sp is the distance function from the p-th stroke. As illustration, Fig. 4 shows the kernel factor (A matrix) for a period of 30 min along the whole length of the line. Then, recursively at each iteration, we remove the oldest information (column W) and include the newest
5. Case of study The method for DSD estimation was applied to a set of transmission lines using historical data from the Colombian Total Lightning Detection System (CTLDS). For this study, ten transmission lines with the largest failure rate in Colombia during 2015 and 2016 were selected [2]. These lines correspond to seven at 220 kV, with lengths between 80 and 195 km and three at 500 kV with lengths between 145 and 212 km. The reported failure rate due to lightning is shown in Table 1. The transmission lines are located in a region with a high ground
Fig. 4. Kernel factor (A matrix) along the transmission line in function of time in a 30 min window. 3
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Table 1 Colombian transmission lines with the largest failure rate due to lightning in Colombia during 2015 and 2016. # failures/100 km Type
Line Length [km]
2015
2016
Line 1 Line 2 Line 3
500 kV
197.4 141.9 212.7
3 3.5 3.8
3 4.9 5.2
Line Line Line Line Line Line Line
220 kV
82.8 86.6 195.1 162.7 136.9 156.0 104.7
10.9 5.8 5.1 3.1 3.7 3.2 10.5
15.7 11.5 2.1 3.7 5.8 5.1 10.5
4 5 6 7 8 9 10
Fig. 7. CTLDS sensors location (dots) and detection efficiency represented by isolines. The highlighted box represent the area of study.
Nowadays, the current network is composed of 21 sensors [15]. Fig. 7 describes the CTLDS sensor locations and the estimated system detection efficiency. The performance of the CTLDS has been discussed in [15,17]. Theoretical detection efficiency in Fig. 7 is computed based on the estimated minimum detectable peak current at each location. Lightning strikes on power transmission lines and the CTLDS location accuracy are studied in [17] by using failure records and physical insulation damages as lightning ground truth reference. The system performance is influenced by the orography of the country; more notoriously at high mountain areas. The detection efficiency for the area of study is between 95% and 99%, and the location accuracy is lower than 300 m. The historical data of 2015 and 2016 have more than 17 million of strokes reported across the Colombian territory. The data were filtered for the region of interest getting approximately 8 million of strokes.
Fig. 6. Ground flash density map for year 2015 and 2016 and transmission line location.
flash density (GFD), as shown in Fig. 6. The Colombian regulation establishes an acceptable outage rate of three failures/100 km for both 500 kV and 220 kV lines. The ground resistance of the lines varies between 5 Ω and 60 Ω. The basic insulation level (BIL) for 500 kV lines is between 1050 and 1500 kV and for 220 kV is between 850 and 1050 kV. This variation is due to the change of altitude on the line path. Both types of lines use a configuration with two shielding wires and horizontal phase configuration for single circuit lines and vertical configuration for double circuit lines. The latter will be the case of lines 3 and 6 and lines 8 and 9. The region is characterized by crossing the Andean mountains, vast river valleys, and coastal plains. Furthermore, this region exposes a significant GFD variation, where the lowest values are registered in high altitudes (more than 2500 MSL), and the highest values are reported on low and medium altitudes (between 0 and 1500 MSL) [15].
5.2. Dynamic stroke density on the line In order to analyze the results of the DSD, for each line, the Lightning-Related-Events (LRE) is identified. We defined an LRE as an event with a DSD value higher than one stroke/line and duration greater than 10 min. Each event could be characterized using the duration and the maximum stroke density, as shown in Fig. 8. In order to compare the DSD in the line, this parameter is normalized to 100 km. The lighting incidence on the line is determined by the number of events and the total time of activity. Table 2 presents the data for each line. Line 7 presents the minimum number of LRE for 2015 and 2016, being 352 and 374 respectively. Line 2 presents the maximum LRE amount with 586 events for 2015 and Line 9 with 639 events for 2016. It is also observed that line 4 has the lowest duration of LRE for 2015 and 2016; however, it is one of the lines with a higher failure rate, as seen in Table 1.
5.1. Lightning location system and historic data The lightning data used in this study is provided by CTLDS, which uses LINET technology [15,16]. This network started operations in 2011 with six sensors located in Colombian territory, and since then it has been upgraded, increasing the number of sensors enhancing coverage, efficiency, and reliability. On 2015, the network had 15 sensors monitoring the Colombian territory with an efficiency higher than 95%. The data used in this analysis correspond to the years 2015 and 2016. 4
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Fig. 10. Boxplot of duration of the LRE in each line. Red central mark indicates the median, the bottom and top edges of the blue box indicate the 25th and 75th percentiles, respectively, up and down blue dots represent percentile 5th and 95th. The whiskers extend to the most extreme data points not considered outliers. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Characteristics of a single event of DSD on a transmission line. Table 2 Number events and the total duration of LRE in transmission lines 2015–2016. events/100 km
Total Duration [days/100 km]
type
2015
2016
2015
2016
Line 1 Line 2 Line 3
500 kV
435 586 522
519 557 606
20.2 21.9 21.5
24.3 25.0 25.2
Line Line Line Line Line Line Line
220 kV
429 477 550 352 559 533 482
478 518 639 374 624 594 525
15.4 24.1 21.7 16.0 18.3 18.3 23.8
18.6 26.6 25.1 18.6 20.7 20.6 24.9
4 5 6 7 8 9 10
distribution where the mean value varies between 4 and 8 Strokes/ 100 km/line, being highest in Lines 5, 7, and 10. The maximum values vary between 100 and 500 Strokes/line, being the line 10 with the highest value. Analyzing the duration of LRE considering a log-normal distribution, as shown in Fig. 10, it is observed that the mean value varies from 40 to 80 min per event per 100 km of line, being highest in lines 4, 5, and 10. The maximum duration is more than 510 min observed in line 4. 5.3. Failure correlation The line failure records were correlated with each LRE analyzing the type of event, the DSD value at the failure moment and the time from the beginning of the LRE to failure time. It is seen in Fig. 11 that the time-to-failure for 500 kV lines failure varies from 2 to 420 min, being the mean value 108 min. The time to
For the total LRE in all lines, the DSD varies from one to 500 strokes/100 km/line. The mean LRE value is 6 strokes, and the 5 and 95% of confidence is 2 and 100 strokes/100 km/line, respectively. In Fig. 9 presents a boxplot with the statistical analysis for the observed events for each line. The data fits better in a log-normal
Fig. 9. Boxplot of maximum density for each event in each line. Red central mark indicates the median, the bottom and top edges of the blue box indicate the 25th and 75th percentiles, respectively, up and down blue dots represent percentile 5th and 95th. The whiskers extend to the most extreme data points not considered outliers, and the red + represent outliers. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 11. Time from the beginning of the LRE up to the registered failure in the line. Red central mark indicates the median, the bottom and top edges of the blue box indicate the 25th and 75th percentiles, respectively, up and down blue dots represent percentile 5th and 95th. The whiskers extend to the most extreme data points not considered outliers, and the red + represent the outliers. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 5
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system, which may increase system awareness and improve power system operation [21], pf could be dependent of time linking it to DSD; nevertheless, more extensive historical data is needed. 7. Conclusions A new method for relating lightning incidence on power transmission lines for real-time purposes was introduced. The DSD concept was developed based on a kernel density estimator where the stroke to distance and time parameters are dynamically integrated into a function that measures the dynamic density as the thunderstorm event progresses. The DSD function was analyzed in this paper by using real thunderstorm cases detected by the CTLDS inside the area of concern of real 220 and 500 kV transmission lines in Colombia with a detailed lightning-related failure score. The proposed dynamic function exposes a high potential ability to identify severe weather and be able to use it in a two-state Markov model for operational analysis purposes. The early detection of lightning risk for transmission lines in the 500 kV level, exposed longer lead times averaging 108 min, with a coherent range from 60 to 190 min. The early risk detection for transmission lines in the 220 kV level, showed an average of 90 min with a quite narrow range between 52 and 120 min. Last difference is plenty explained by the different insulation and immunity levels of both systems and indicates that specific DSD patterns can be estimated for power networks in all voltage levels. Initial results show that the transmission failure rate could not fully explain with density parameters. Therefore, future work should be performed to improve probability failure function dependent on DSD values, and other influencing parameters, in order to achieve dynamical reliability in power systems which may improve situational awareness or system operation.
Fig. 12. DSD value on the moment of the registered failure in the line. Red central mark indicates the median, the bottom and top edges of the blue box indicate the 25th and 75th percentiles, respectively, up and down blue dots represent percentile 5th and 95th. The whiskers extend to the most extreme data points not considered outliers.
failure in 220 kV lines occurs between 2 min up to 250 min with a mean time 90 min. Most of the failures in 220 kV occur faster than 500 kV. It could be explained due to 500 kV has more significant insulation level. In Fig. 12 is shown the DSD value when a failure was registered on the transmission line. The mean value for 500 kV lines is 9 strokes/ 100 km/line and for 220 kV lines is approximately 20 strokes/100 km/ line. Transmission lines 4, 5, and 10 present a failure rate up above the acceptable one. The average and maximum DSD values for the LRE of these lines are higher for the rest of the analyzed lines. However, this reason, can not be conclusive, and further analysis should be performed to analyze in detailed other influencing parameters such as groundings, insulator maintenance, lightning currents, among others.
Declaration of Competing Interest There are no conflict of interest in this work.
6. Possible power system applications
Acknowledgment
Currently, the traditional power system is becoming smarter with the concept of smart grid, where the interaction with information makes it capable of taking decisions that improve efficiency, reliability, costs, resiliency, among others [18,19]. One of the major issues on a power system is to predict failures due to external variables, such as lightning. In this case, with DSD parameter, it is possible to use a twostate Markov model, establishing a probability of failure during fair weather and other in severe weather [20]. Severe weather is related to high lightning activity with the potential to generate a transmission line failure. In this case, a probability line failure pf , which may depend on weather could be defined as follows. The proposed model could be expressed as (16)
The authors wish to thank the Colombian Administrative Department of Science and Technology - COLCIENCIAS who finance part of this research with contract No FP44842-051-2016. Also would like to thank INTERCOLOMBIA S.A. E.S.P for providing part of the data used for this research.
pf (t ) =
N+S ⎧ λi N (1 ⎨ λi N + S F S ⎩
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijepes.2019.105527. References
− F ) DSD < 1[Stroke] DSD > 1[Stroke]
[1] Castillo A. Risk analysis and management in power outage and restoration: a literature survey. Electr Power Syst Res 2014;107:9–15. https://doi.org/10.1016/j. epsr.2013.09.002. [2] Muñetones E, Pérez E, Aranguren D, Tovar C, Herrera J, Torres H, et al. International conference on grounding and earthing & 8th international conference on lightning physics and effects Pirenópolis, Brazil - May, 2018. In: Proceedings of international conference on grounding and earthing; 2018. p. 6. [3] Hileman AR. Insulation coordination for power systems, power engineering (Willis). 1st ed. CRC Press/Taylor & Francis Group; 1999. [4] I.S. 1243-1997. IEEE guide for improving the lightning performance of transmission lines. IEEE Std 1243-1997; 1997. p. 1–44. https://doi.org/10.1109/IEEESTD.1997. 84660. [5] W.C. SC C4. Lightning parameters for engineering applications, CIGRE; 2013. [6] IEC 62793:2016 Protection against lightning - Thunderstorm warning systems, 1st ed., IEC - International Electrotechnical Commission, Switzertland; 2016. [7] Heitkemper LJ, Price RF, Johnson DB. Lightning-warning systems for use by
(16)
where λi is the failure average rate of line i based on historical data. N and S, is the duration time of fair and severe weather respectively. F is the failure proportion during severe weather. Using the data of Line 4 for the number of failures and duration according to Tables 1 and 2, it is computed an average duration of severe weather of 14,1 days/year for 2015 and 2016. The average failures due to lightning is 11 faults/year, where 70% of failures are due to lightning. As a result, the probability of failure during severe weather is 58 times greater than fair weather. As a future step, in order to evaluate dynamic reliability in the 6
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
On the development of dynamic stroke density for transmission line for power system operational applications
T
⁎
Ernesto Pereza, , Jairo Espinosaa, Daniel Arangurenb a b
Universidad Nacional de Colombia, Departamento de Energía Eléctrica y Automática, Medellín, Colombia Keraunos S.A.S, Colombia
A R T I C LE I N FO
A B S T R A C T
Keywords: Lightning parameters Lightning location systems Tropical regions Lightning density maps Keraunic level Parameter estimation
This paper proposes a method to estimate the impact of lightning activity on transmission lines. The method uses a time-variant density parameter described using kernel basis functions. The algorithm is implemented and tested with historical data in real transmission lines located in Colombia for the years 2015 and 2016. Statistical analysis is performed to observe the lightning activity on each line, characterizing its severity in density magnitude and the duration of it. The correlation of this parameter with the line failures is also analyzed. Finally, the paper concludes that this parameter could be useful for applications on a real-time operation.
1. Introduction Electric power systems are critical infrastructure because the society and economy are dependable of it. Besides, the electric power system is indispensable for other critical systems, such as gas infrastructure, water supply, financial, services, telecommunications, public health, transportation, among others [1]. Lightning is one of the major causes of failure in electric power systems, where, according to several authors, more than 60% of the transmission lines failures are due to this phenomenon [2]. Traditionally, power system infrastructure is protected against lightning through insulation coordination techniques, which may include insulation level enhancement, shielding wires, and surge protective devices [3,4]. This methodology is based mainly on information, voltage rate, environmental conditions, and ground flash density. The lightning information is gathered on a keraunic level or Lightning Location Systems, being more reliable the latter [5]. The traditional design only uses the ground flash density as an average of yearly basis information, neglecting the dynamical behavior of thunderstorms. Nowadays, lightning location systems installed all over the world provide real-time data which create new possibilities for operational uses in different sectors. Two main government bodies had addressed the good practices: The IEC62793 standard [6], which deals with the framework of thunderstorm warning systems and the implementation of preventive hazard measures, and the Federal Aviation Administration (FAA), in the ACRP report eight [7] deals with lightning warning systems focused on airports.
⁎
Recently Tong et al. [8] proposed the concept of Dynamic Lightning Protection (DLP), which is an operational concept where the lightning activity is taken into account to take preventive actions to reduce the possibility of power outages. The warning process used is based on the two area concept, defined in the IEC62793 standard [6]. The two area concept for warning defines two areas: one called area of concern (AOC) containing the infrastructure to be protected, and other called area of warning (AOW), which encloses the AOC. A warning will be triggered once lightning strikes inside the AOW and is turned off if no strikes are detected in the AOW after a given dwell-time. This concept is very useful; however, it may produce a large number of false alarms [9]. The general lightning-related failure risk of power lines is commonly simplified by the assumption of simple collecting area and the calculation of a flash collection rate as given in IEEE 1243 standard ec (1) [10], based on a constant Ground Flash Density obtained from historical multi-annual values.
28h0.6 + b ⎞ Ns = Ng ⎛⎜ ⎟ 10 ⎠ ⎝
(1)
where Ng is the Ground Flash Density Ns is the flashes/100 km/year h is the tower height b is the separation distance between the external ground or phase wires. The approach in this paper considers a real-time calculation of the lightning risk based on a dynamic concept of the lightning (stroke) density. The proposed methodology is intended to provide a dynamic estimation of the impact of lightning activity on transmission lines.
Corresponding author at: Cra 80, No 65-223, M8-205, Facultad de Minas, Medellín, Colombia. E-mail addresses: [email protected] (E. Perez), [email protected] (J. Espinosa), [email protected] (D. Aranguren).
https://doi.org/10.1016/j.ijepes.2019.105527 Received 16 April 2019; Received in revised form 6 July 2019; Accepted 1 September 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
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Furthermore, the paper presents a correlation between the proposed dynamic parameter and line failures. This paper is organized as follows: Section 2 describes and define the concept of dynamic stroke density (DSD). The implementation algorithm is presented in Section 3. Section 4 makes a description of the vulnerability of transmission lines. Statistical analysis for the DSD on real transmission lines is analyzed in Section 5. In Section 6 is presented possible applications for real-time uses in power system operation. Finally, conclusions are presented in Section 7. 2. Transmission line dynamic stroke density We define transmission line DSD as a function in time and lightning activity. First, we estimate the stroke density on the transmission line based on a kernel density estimator [11] which is being implemented by several authors in different applications [12–14]. As a basic concept, we use for each stroke a kernel function K: → that satisfies the condition of Eq. (2).
Fig. 2. Representation of transmission line by means of piece-wise linear segments.
∞
∫−∞ Ki (s) ds = 1
(2) path and will not be a perfect straight segment. In this case, we can represent the line as a linear piece-wise path as shown in Fig. 2. Integrating each straight segment to find the density d as expressed in Eq. (7).
where s is the variable in space. For our case we use a Gaussian kernel given by Eq. (2) s2
K (s ) =
− 1 e 2σs2 σs 2π
(3)
M
d=
where σs is the standard deviation of distance, also known as smoothing parameter, and s is the distance from the stroke. We can establish that the range of influence of a stroke is approximately 3σs . The magnitude of σs must be larger than the lightning location accuracy. The density function for each stroke for a given transmission line, as shown in Fig. 1, can be expressed as (6). The stroke density along the line di varies between 0 and 1 as a function of s.
di =
∫C K (s) dl
⎡Stroke/line⎤ ⎥ ⎢ ⎦ ⎣
∫0
1
K (λ ) dλ
⎡Stroke/line⎤ ⎥ ⎢ ⎦ ⎣
K
⎞ ⎞ ⎛⎛ 1 − λ aj + λbj dλ ⎟ ⎟ ⎜⎜ ⎠ ⎠ ⎝⎝
(7)
where aj and bj are the extremes of the straight segment. For a Gaussian kernel the expression may be written in terms of erf: M
d=
2π σs ⎡ ⎛ 2 ⎛ ⎞⎞ ⎛ 2 s ⎟⎞⎤ erf ⎜ ⎜sa + Δl j ⎟ ⎟ − erf ⎜ aj ⎥ 4Δl j ⎢ ⎝ 2σs ⎝ j ⎠⎠ ⎝ 2σs ⎠⎦ ⎣
∑ j=1
(8)
where Δl j = aj − bj is the straight distance between the points aj and bj , and the erf function is:
(4)
2 π
erf(x ) =
∫0
x
2
e−t dt
(9)
The density described above is static and does not take into account the time evolution of the lightning activity, for this reason, we proposed to multiply the calculated density with a decaying time function as shown in (10).
(5)
Therefore, the density along the path is:
di =
1
j=1
where C is the contour of the function l (λ ) describing the path of the transmission line from the beginning (λ = 0 ) till the end (λ = 1). The function relating s and λ is given by
s (λ )2 = l (0)T l (0) + 2l (0)T l (λ ) + l (λ )T l (λ )
∑ ∫0
di (t ) =
(6)
In real configurations, a transmission line will have an irregular
∫0
1
K (λ ) dλfi (t ) ⎡Stroke/line⎤ ⎥ ⎢ ⎦ ⎣
(10)
where f (t ) be any decreasing function that represents the reducing factor of density in time so that new strokes contribute more on the density than old strokes. In our case we define a exponential function as shown in Eq. (11).
fi (t ) = e−
(t − ti) τ
(11)
where ti is the time of occurrence of the stroke, t is the current time and τ is decay constant. The total density along the line for N strokes on the vicinity of the line will be: N
D (t ) =
∑ i=1
di (t )
(12)
where i denotes each stroke. Since D is a function of distance, time, and the number of strokes, this factor implicitly comprises the evolution of lightning rate and the vicinity of lightning activity. The exponential function of time allows giving more importance to the recent strokes and less significance to old ones.
Fig. 1. Geometrical configuration of lightning strike and straight transmission line. 2
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Fig. 5. Characteristics of the dynamic stroke density D (t ) for a transmission line during a thunderstorm event.
Fig. 3. Lightning activity near a transmission line with an observation time window of 30 min. Yellow dots represent each stroke. Blue line represents a 500 kV transmission line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
one (column 1). The parameters used for the case of analysis are: σs = 10 [km], tw = 30 [min], Δt = 1 [min], Ll = 500 [m]. Once the instantaneous value of the kernel is calculated for the time window and along the length, it must be weighted with the time factor shown in Eq. (11). In order to do so, we will create a vector T ∈ RN with entries:
3. Dynamic stroke density estimation algorithm The proposed concept is implemented to analyze lightning data and real transmission lines. It uses real-time data provided by the lightning location system, as shown in Fig. 3. This procedure has the following steps: The transmission line tower location is read, obtaining M segments of a defined length of Ll . Every Δt , the database is queried for all strokes that occurred in the previous period. Only the strokes within a 4σs distance to the lines are selected for the estimation of the density using (6) for each segment of the line. The information is stored in a matrix A ∈ RM × W for a time window tw , where W = tw /Δt . Therefore the entries of the matrix A (t ) will be computed as:
∑ p=1
⎦
(14)
Finally the density D (t ) for a given line is computed as:
D (t ) = A (t ) T
1
(15)
where . 1 denotes the norm-1 of the vector or the sum of the absolute values of the entries of the vector. Fig. 5 shows the values of the D (t ) 4. Vulnerability
P (t − (j − 1)Δt )
Ai, j (t ) =
−(W − 1)Δt T −Δt ⎤ τ , …, e τ
T = ⎡1, e ⎣
∫a
bi
i
⎛ ⎞ K sp (l) dl ⎜ ⎟ ⎝ ⎠
The failure condition of power transmission lines is finally dependent on the hazard severity, computed as previously described; but also on the system vulnerability given by the insulation level, overvoltage protection elements, grounding values, materials, among many others. Electromagnetic transient analyses would be necessary to understand how a given condition of direct or indirect lightning incidence causes a given failure condition such as a back flashover, shielding failure flashover or other. Such scenarios represent a wide number of possible combinations and situations. The vulnerability can be alternatively understood as the cause-effect relation derived from the dynamic risk behavior, as previously discussed, and the historical performance of the real power transmission system, that is also dynamic. This approach does not allow to keep visible all the details of the electromagnetic phenomenon but leads to understanding useful and more practical patterns of the system performance. Next section goes deeper in the described approach.
(13)
where P (t − (j − 1)Δt ) is the number of strokes in the time window of t − j Δt < t ⩽ t − (j − 1)Δt , ai and bi are the extremes of the i-th line segment, and sp is the distance function from the p-th stroke. As illustration, Fig. 4 shows the kernel factor (A matrix) for a period of 30 min along the whole length of the line. Then, recursively at each iteration, we remove the oldest information (column W) and include the newest
5. Case of study The method for DSD estimation was applied to a set of transmission lines using historical data from the Colombian Total Lightning Detection System (CTLDS). For this study, ten transmission lines with the largest failure rate in Colombia during 2015 and 2016 were selected [2]. These lines correspond to seven at 220 kV, with lengths between 80 and 195 km and three at 500 kV with lengths between 145 and 212 km. The reported failure rate due to lightning is shown in Table 1. The transmission lines are located in a region with a high ground
Fig. 4. Kernel factor (A matrix) along the transmission line in function of time in a 30 min window. 3
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Table 1 Colombian transmission lines with the largest failure rate due to lightning in Colombia during 2015 and 2016. # failures/100 km Type
Line Length [km]
2015
2016
Line 1 Line 2 Line 3
500 kV
197.4 141.9 212.7
3 3.5 3.8
3 4.9 5.2
Line Line Line Line Line Line Line
220 kV
82.8 86.6 195.1 162.7 136.9 156.0 104.7
10.9 5.8 5.1 3.1 3.7 3.2 10.5
15.7 11.5 2.1 3.7 5.8 5.1 10.5
4 5 6 7 8 9 10
Fig. 7. CTLDS sensors location (dots) and detection efficiency represented by isolines. The highlighted box represent the area of study.
Nowadays, the current network is composed of 21 sensors [15]. Fig. 7 describes the CTLDS sensor locations and the estimated system detection efficiency. The performance of the CTLDS has been discussed in [15,17]. Theoretical detection efficiency in Fig. 7 is computed based on the estimated minimum detectable peak current at each location. Lightning strikes on power transmission lines and the CTLDS location accuracy are studied in [17] by using failure records and physical insulation damages as lightning ground truth reference. The system performance is influenced by the orography of the country; more notoriously at high mountain areas. The detection efficiency for the area of study is between 95% and 99%, and the location accuracy is lower than 300 m. The historical data of 2015 and 2016 have more than 17 million of strokes reported across the Colombian territory. The data were filtered for the region of interest getting approximately 8 million of strokes.
Fig. 6. Ground flash density map for year 2015 and 2016 and transmission line location.
flash density (GFD), as shown in Fig. 6. The Colombian regulation establishes an acceptable outage rate of three failures/100 km for both 500 kV and 220 kV lines. The ground resistance of the lines varies between 5 Ω and 60 Ω. The basic insulation level (BIL) for 500 kV lines is between 1050 and 1500 kV and for 220 kV is between 850 and 1050 kV. This variation is due to the change of altitude on the line path. Both types of lines use a configuration with two shielding wires and horizontal phase configuration for single circuit lines and vertical configuration for double circuit lines. The latter will be the case of lines 3 and 6 and lines 8 and 9. The region is characterized by crossing the Andean mountains, vast river valleys, and coastal plains. Furthermore, this region exposes a significant GFD variation, where the lowest values are registered in high altitudes (more than 2500 MSL), and the highest values are reported on low and medium altitudes (between 0 and 1500 MSL) [15].
5.2. Dynamic stroke density on the line In order to analyze the results of the DSD, for each line, the Lightning-Related-Events (LRE) is identified. We defined an LRE as an event with a DSD value higher than one stroke/line and duration greater than 10 min. Each event could be characterized using the duration and the maximum stroke density, as shown in Fig. 8. In order to compare the DSD in the line, this parameter is normalized to 100 km. The lighting incidence on the line is determined by the number of events and the total time of activity. Table 2 presents the data for each line. Line 7 presents the minimum number of LRE for 2015 and 2016, being 352 and 374 respectively. Line 2 presents the maximum LRE amount with 586 events for 2015 and Line 9 with 639 events for 2016. It is also observed that line 4 has the lowest duration of LRE for 2015 and 2016; however, it is one of the lines with a higher failure rate, as seen in Table 1.
5.1. Lightning location system and historic data The lightning data used in this study is provided by CTLDS, which uses LINET technology [15,16]. This network started operations in 2011 with six sensors located in Colombian territory, and since then it has been upgraded, increasing the number of sensors enhancing coverage, efficiency, and reliability. On 2015, the network had 15 sensors monitoring the Colombian territory with an efficiency higher than 95%. The data used in this analysis correspond to the years 2015 and 2016. 4
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Fig. 10. Boxplot of duration of the LRE in each line. Red central mark indicates the median, the bottom and top edges of the blue box indicate the 25th and 75th percentiles, respectively, up and down blue dots represent percentile 5th and 95th. The whiskers extend to the most extreme data points not considered outliers. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Characteristics of a single event of DSD on a transmission line. Table 2 Number events and the total duration of LRE in transmission lines 2015–2016. events/100 km
Total Duration [days/100 km]
type
2015
2016
2015
2016
Line 1 Line 2 Line 3
500 kV
435 586 522
519 557 606
20.2 21.9 21.5
24.3 25.0 25.2
Line Line Line Line Line Line Line
220 kV
429 477 550 352 559 533 482
478 518 639 374 624 594 525
15.4 24.1 21.7 16.0 18.3 18.3 23.8
18.6 26.6 25.1 18.6 20.7 20.6 24.9
4 5 6 7 8 9 10
distribution where the mean value varies between 4 and 8 Strokes/ 100 km/line, being highest in Lines 5, 7, and 10. The maximum values vary between 100 and 500 Strokes/line, being the line 10 with the highest value. Analyzing the duration of LRE considering a log-normal distribution, as shown in Fig. 10, it is observed that the mean value varies from 40 to 80 min per event per 100 km of line, being highest in lines 4, 5, and 10. The maximum duration is more than 510 min observed in line 4. 5.3. Failure correlation The line failure records were correlated with each LRE analyzing the type of event, the DSD value at the failure moment and the time from the beginning of the LRE to failure time. It is seen in Fig. 11 that the time-to-failure for 500 kV lines failure varies from 2 to 420 min, being the mean value 108 min. The time to
For the total LRE in all lines, the DSD varies from one to 500 strokes/100 km/line. The mean LRE value is 6 strokes, and the 5 and 95% of confidence is 2 and 100 strokes/100 km/line, respectively. In Fig. 9 presents a boxplot with the statistical analysis for the observed events for each line. The data fits better in a log-normal
Fig. 9. Boxplot of maximum density for each event in each line. Red central mark indicates the median, the bottom and top edges of the blue box indicate the 25th and 75th percentiles, respectively, up and down blue dots represent percentile 5th and 95th. The whiskers extend to the most extreme data points not considered outliers, and the red + represent outliers. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 11. Time from the beginning of the LRE up to the registered failure in the line. Red central mark indicates the median, the bottom and top edges of the blue box indicate the 25th and 75th percentiles, respectively, up and down blue dots represent percentile 5th and 95th. The whiskers extend to the most extreme data points not considered outliers, and the red + represent the outliers. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 5
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system, which may increase system awareness and improve power system operation [21], pf could be dependent of time linking it to DSD; nevertheless, more extensive historical data is needed. 7. Conclusions A new method for relating lightning incidence on power transmission lines for real-time purposes was introduced. The DSD concept was developed based on a kernel density estimator where the stroke to distance and time parameters are dynamically integrated into a function that measures the dynamic density as the thunderstorm event progresses. The DSD function was analyzed in this paper by using real thunderstorm cases detected by the CTLDS inside the area of concern of real 220 and 500 kV transmission lines in Colombia with a detailed lightning-related failure score. The proposed dynamic function exposes a high potential ability to identify severe weather and be able to use it in a two-state Markov model for operational analysis purposes. The early detection of lightning risk for transmission lines in the 500 kV level, exposed longer lead times averaging 108 min, with a coherent range from 60 to 190 min. The early risk detection for transmission lines in the 220 kV level, showed an average of 90 min with a quite narrow range between 52 and 120 min. Last difference is plenty explained by the different insulation and immunity levels of both systems and indicates that specific DSD patterns can be estimated for power networks in all voltage levels. Initial results show that the transmission failure rate could not fully explain with density parameters. Therefore, future work should be performed to improve probability failure function dependent on DSD values, and other influencing parameters, in order to achieve dynamical reliability in power systems which may improve situational awareness or system operation.
Fig. 12. DSD value on the moment of the registered failure in the line. Red central mark indicates the median, the bottom and top edges of the blue box indicate the 25th and 75th percentiles, respectively, up and down blue dots represent percentile 5th and 95th. The whiskers extend to the most extreme data points not considered outliers.
failure in 220 kV lines occurs between 2 min up to 250 min with a mean time 90 min. Most of the failures in 220 kV occur faster than 500 kV. It could be explained due to 500 kV has more significant insulation level. In Fig. 12 is shown the DSD value when a failure was registered on the transmission line. The mean value for 500 kV lines is 9 strokes/ 100 km/line and for 220 kV lines is approximately 20 strokes/100 km/ line. Transmission lines 4, 5, and 10 present a failure rate up above the acceptable one. The average and maximum DSD values for the LRE of these lines are higher for the rest of the analyzed lines. However, this reason, can not be conclusive, and further analysis should be performed to analyze in detailed other influencing parameters such as groundings, insulator maintenance, lightning currents, among others.
Declaration of Competing Interest There are no conflict of interest in this work.
6. Possible power system applications
Acknowledgment
Currently, the traditional power system is becoming smarter with the concept of smart grid, where the interaction with information makes it capable of taking decisions that improve efficiency, reliability, costs, resiliency, among others [18,19]. One of the major issues on a power system is to predict failures due to external variables, such as lightning. In this case, with DSD parameter, it is possible to use a twostate Markov model, establishing a probability of failure during fair weather and other in severe weather [20]. Severe weather is related to high lightning activity with the potential to generate a transmission line failure. In this case, a probability line failure pf , which may depend on weather could be defined as follows. The proposed model could be expressed as (16)
The authors wish to thank the Colombian Administrative Department of Science and Technology - COLCIENCIAS who finance part of this research with contract No FP44842-051-2016. Also would like to thank INTERCOLOMBIA S.A. E.S.P for providing part of the data used for this research.
pf (t ) =
N+S ⎧ λi N (1 ⎨ λi N + S F S ⎩
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijepes.2019.105527. References
− F ) DSD < 1[Stroke] DSD > 1[Stroke]
[1] Castillo A. Risk analysis and management in power outage and restoration: a literature survey. Electr Power Syst Res 2014;107:9–15. https://doi.org/10.1016/j. epsr.2013.09.002. [2] Muñetones E, Pérez E, Aranguren D, Tovar C, Herrera J, Torres H, et al. International conference on grounding and earthing & 8th international conference on lightning physics and effects Pirenópolis, Brazil - May, 2018. In: Proceedings of international conference on grounding and earthing; 2018. p. 6. [3] Hileman AR. Insulation coordination for power systems, power engineering (Willis). 1st ed. CRC Press/Taylor & Francis Group; 1999. [4] I.S. 1243-1997. IEEE guide for improving the lightning performance of transmission lines. IEEE Std 1243-1997; 1997. p. 1–44. https://doi.org/10.1109/IEEESTD.1997. 84660. [5] W.C. SC C4. Lightning parameters for engineering applications, CIGRE; 2013. [6] IEC 62793:2016 Protection against lightning - Thunderstorm warning systems, 1st ed., IEC - International Electrotechnical Commission, Switzertland; 2016. [7] Heitkemper LJ, Price RF, Johnson DB. Lightning-warning systems for use by
(16)
where λi is the failure average rate of line i based on historical data. N and S, is the duration time of fair and severe weather respectively. F is the failure proportion during severe weather. Using the data of Line 4 for the number of failures and duration according to Tables 1 and 2, it is computed an average duration of severe weather of 14,1 days/year for 2015 and 2016. The average failures due to lightning is 11 faults/year, where 70% of failures are due to lightning. As a result, the probability of failure during severe weather is 58 times greater than fair weather. As a future step, in order to evaluate dynamic reliability in the 6
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