Probabilistic Approach in Evaluation of Backflashover ...

Probabilistic Approach in Evaluation of Backflashover in 230kV Double Circuit Transmission Line Saeed Mohajeryami, Milad Doostan University of North Carolina at Charlotte Department of Electrical and Computer Engineering Chrlotte, NC {smohajer, mdoostan}@uncc.com

Abstract- In order to study the problems posed by lightning stroke on vastly exposed transmission lines, it is essential to study different lightning overvoltage phenomena. One of the most significant electrical transients caused by lightning is backflashover. In this paper, by applying Monte Carlo method and considering accurate models of transmission line, grounding system and physical model of breakdown in insulator gap, the backflashover is studied on a 230 kV double circuit transmission line. To apply the proposed approach, the selected case study is simulated in EMTP-RV software and the results are presented. Index Terms—Backflashover, Lightning Overvoltage, Leader propagation model, Monte Carlo, EMTP-RV I. INTRODUCTION

huge financial losses caused by power equipment failures of transmission lines (TL) has necessitated the need for paying attention to these widely exposed lines which are subject to vast variety of faults. One of the most frequent faults occurring at the transmission lines are outages caused by the lightning strikes [1]. For a better understanding of the problems posed by lightning strokes, it is crucial to do research on a phenomenon called backflashover. When a direct lightning strikes the tower of an overhead power line, it produces a transient voltage which moves through the tower and reflects to the tower top from tower footing resistance. If voltages across the tower cross arms built up by these multiple reflections, equal or exceed the insulator withstand capability, backflashover will occur [2]. Because of this overvoltage with high amplitude and extremely high steepness [1], different problems including the equipment failure [3], reliability reduction and phase to ground faults may arise [1]. Moreover, the insulation design of varied devices is considerably based on lightning overvoltage in the network [4]. The evaluation of lightning is essential to get around those aforementioned issues. A wide variety of methods have been proposed and utilized to evaluate lightning

performance. One estimating method which uses a constant 2 𝜇𝜇𝜇𝜇 front was proposed by Anderson [5]. Later on, IEEE working group published a simplified method by modifying the previous aforesaid method [6]. Tokyo Electric Power Company has performed a study to observe waveforms of lightning stroke on 60 transmission lines and has developed a quantitative evaluation of characteristics of lightning waveforms parameters [7]. Lightning and some line parameters such as phase angle of power frequency voltage at the lightning stroke instance have a random nature; therefore, it is necessary to select a method which takes these arbitrary natures into account. Hence, lots of statistical methods are employed in the literature, one of which is application of Monte Carlo method. Indeed, this approach can handle uncertainties introduced by random nature of these parameters and can help to make useful predictions for evaluation of transmission lines lightning performance [8-10]. In this paper, by applying Monte Carlo method and considering accurate models of transmission line, grounding system and physical model of breakdown in insulator gap, the backflashover phenomenon is studied in a 230 kV double circuit transmission line. To apply the proposed approach, a case study of a transmission line located between Lushan and Deilaman cities in Iran has been selected. In what follows, a description of the case study TL is provided in section II. Monte Carlo method is introduced in detail in section III. Models of varied parameters are presented in section IV. Section V presents the results of the simulation in EMTP-RV software. Finally, the discussion and conclusion of the results are presented in section VI. II.

BRIEF DESCRIPTION OF TEST LINE

As it was mentioned, Lushan- Deilaman transmission line is a high voltage 230 kV double circuit TL which is

located in Gilan Province in Iran. According to national weather bureau, the area experiences the average of 25 thunderstorm day annually. The conductor and shield wire information of the line are summarized in Table I. TABLE I. CONDUCTOR AND SHIELD WIRE DATA

Name Type Number of Strands Diameter (mm) Total Area(mm2) DC Resistance(Ω/km) GMR(cm)

Conductor Canary AA 54 29.52 515.16 0.0635 1.1332

Shield Wire Canary --1 9.84 --3.24 ---

The other information of TL is briefly as follows: Line length: 65 km Ruling span: 300m Lightning outage rate: 1.5 per 100Km per year Insulator gap length: 2112mm Tower footing resistance: 20 ohm maximum Soil resistivity: 100-150 Ohm. Meter Moreover, this line is mostly consist of DC0 type towers. Figure 1 shows tower structure, phase and shield wire configuration.

significant uncertainty in inputs such as evaluation of lightning performance. As it was mentioned previously, lightning has a random nature. Indeed, lightning parameters including current crest, rise time, tail time and phase angel of power frequency voltage at stroke instance are parameters which have random nature. Table II, summarizes the statistical characteristics of these parameters. TABLE II. STATISTICAL CHARACTERISTICS OF THE LIGHTNING PARAMETERS.

Parameter PDF 𝒙𝒙𝒎𝒎 𝝈𝝈 Log-normal Rise time 2𝜇𝜇𝜇𝜇 0.4943𝜇𝜇𝜇𝜇 Log-normal 77.5𝜇𝜇𝜇𝜇 0.577𝜇𝜇𝜇𝜇 Tail time 34 kA 0.74 kA Current crest Log-normal Uniform Between 0 to 360 Phase angle It is assumed that the current crest, rise time and tail time follow a log-normal distribution with PDF function of p(x) [12-13]. 𝑃𝑃(𝑥𝑥) =

1

𝑥𝑥𝑥𝑥√2𝜋𝜋

𝑒𝑒

−(ln 𝑥𝑥−ln 𝑥𝑥𝑚𝑚 )2 2𝜎𝜎 2

(1)

𝜎𝜎 ≥ 0 , − ∞ ≤ ln 𝑥𝑥𝑚𝑚 ≤ +∞ Where, Ln ( 𝑥𝑥𝑚𝑚 ) and 𝜎𝜎 are mean and standard deviation of natural logarithm of X. Figures 2-4 illustrate the probability function of parameters with log-normal distribution. IV.

MODELING

A. Lightning current source model In order to calculate lightning outage rate, the probability of exceeding stroke of current, I, is needed. This probability distribution function can approximately be computed from equation (2) [14]. 𝑃𝑃𝐼𝐼 = Figure 1 DC0 type tower structure III.

MONTE CARLO

The Monte Carlo methods are a broad class of computational algorithms that are concerned with making useful predictions from situations containing random processes [11]. In fact, these methods are based on an iterative procedure that in each step uses a set of values which are generated for problem variables according to their probability density function (PDF). Monte Carlo methods are useful in solving multidimensional complex problems either stochastic or deterministic ones where it is impossible to apply other mathematical approaches. One example of their application includes modeling phenomena with

1 𝐼𝐼 1 + ( )2.6 31

(2)

In this paper, double exponential formula which is provided in equation (3) has been employed to model the current source [14]. 𝑖𝑖(𝑡𝑡) = 1.04𝐼𝐼𝑚𝑚 (𝑒𝑒

𝑡𝑡 − 𝑇𝑇1

𝑇𝑇1 = 1.365434𝑇𝑇𝑅𝑅

𝑇𝑇𝑠𝑠 𝑇𝑇2 = 2.282835

− 𝑒𝑒

−

𝑡𝑡 𝑇𝑇2 )

(3)

(4)

(5)

Where 𝑇𝑇𝑠𝑠 is “rise time” and 𝑇𝑇𝑅𝑅 is “tail time”. Indeed, as the positive polarity lightning stroke is nearly 5% of all strokes, it is neglected in this work. Moreover, the impedance of the lightning discharge channel is assumed to be 400Ω.

Figure 2 Log-normal distribution of lightning current rise time

Figure 5 Multistory tower model

Fig. 6 Tower shape to calculate tower surge impedance

Table III summarizes the computed parameters and their formulas. TABLE III. MULTISTORY TOWER MODEL PARAMETERS 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 179.2 𝑍𝑍𝑡𝑡1 = 𝑍𝑍𝑡𝑡2 = 𝑍𝑍𝑡𝑡3 = 1.19𝑍𝑍 = 213.2 𝑍𝑍𝑡𝑡4 = 0.81𝑍𝑍 = 145.15 𝑣𝑣𝑡𝑡1 = 𝑣𝑣𝑡𝑡2 = 𝑣𝑣𝑡𝑡3 = 𝑣𝑣𝑡𝑡4 = 𝑣𝑣 = 300 𝛾𝛾 = 0.8944 𝜏𝜏 = 2𝐻𝐻⁄𝑣𝑣=0.28 𝑟𝑟1 = −(2 × 𝑍𝑍𝑡𝑡1 × ln 𝛾𝛾)/(ℎ1 + ℎ2 + ℎ3 ) = 2.88 𝑟𝑟2 = −(2 × 𝑍𝑍𝑡𝑡4 × ln 𝛾𝛾)/ℎ4 = 1.29 𝑅𝑅1 = 𝑟𝑟1 × ℎ1 = 11.5 𝑅𝑅2 = 𝑟𝑟1 × ℎ2 = 18.1 𝑅𝑅3 = 𝑟𝑟1 × ℎ3 = 18.4 𝑅𝑅4 = 𝑟𝑟2 × ℎ4 = 32.5 𝐿𝐿1 = 𝑅𝑅1 × 𝜏𝜏 = 3.22 𝐿𝐿2 = 𝑅𝑅2 × 𝜏𝜏 = 5.06 𝐿𝐿3 = 𝑅𝑅3 × 𝜏𝜏 = 5.15 𝐿𝐿4 = 𝑅𝑅4 × 𝜏𝜏 = 9.1

Figure 3 Log-normal distribution of lightning current tail time

Figure 4

Log-normal distribution of lightning current crest

B. Tower and Transmission line model By considering phase coupling, the frequencydependent model in EMTP-RV is utilized to build the model of double circuit TL. In addition, the multistory model [16] is used for tower model depicted in Figure 5. CIGRE recommended equation of (6) could be used to calculate the tower surge impedance [14]. Since the structure of DC0 vertical tower is almost the same as the tower used in [16], the same ratio has been chosen for dividing surge impedance between upper and lower halves. 𝑅𝑅

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 60 ln �cot �0.5 tan−1 � ��� ℎ

(6)

Where: 𝑅𝑅 =

𝑟𝑟1 ℎ2 + 𝑟𝑟2 ℎ + 𝑟𝑟3 ℎ1 , ℎ = ℎ1 + ℎ2 ℎ

(7)

From equation (7), it is understood that the height and radius are needed to compute the surge impedance. According to tower structure, these values are shown in Figure 6.

[Ω] [Ω] [Ω] [m/𝜇𝜇𝜇𝜇] [𝜇𝜇𝜇𝜇] [Ω/m] [Ω/m] [Ω] [Ω] [Ω] [Ω] [𝜇𝜇𝜇𝜇] [𝜇𝜇𝜇𝜇] [𝜇𝜇𝜇𝜇] [𝜇𝜇𝜇𝜇]

C. Tower footing resistance model A vast variety of methods have been proposed to calculate the tower footing resistance while there are fast transient surges which can ionize the soil and change the resistance. However, one of the most simple and practical approaches which take the surges considerations into account is provided by CIGRE [14]. According to this method the tower footing resistance could be calculated from equation (8). RF =

𝑅𝑅0

𝐼𝐼 �1 + 𝐼𝐼 𝑔𝑔

(8)

Where: 𝑅𝑅0: Tower footing resistance at low current and low frequency (ohm),𝐼𝐼𝑔𝑔 : Limiting current initiating soil ionization (kA) which can be calculated by equation (9): Ig =

1 𝐸𝐸0 . 𝜌𝜌 . 2𝜋𝜋 𝑅𝑅02

(9)

Where 𝜌𝜌 is soil resistivity (ohm-meter), and 𝐸𝐸0 is soil ionization gradient (about 400 kV/m).

D. Backflashover Model Insulation coordination is typically based on standard impulse voltage (1.5/50 micro sec); nevertheless, it is critical that insulation performance is determined while it is stressed by non-standard lightning impulse. From comprehensive physical analysis, it is noticed that discharge development is composed of three different phases of corona inception, streamer propagation and leader propagation. Consequently, as it is shown in equation (10) the time-to-breakdown, 𝑡𝑡𝑏𝑏 , could be represented as a sum of three components[14]. 𝑇𝑇b = 𝑡𝑡𝑖𝑖 + 𝑡𝑡𝑠𝑠 + 𝑡𝑡𝑙𝑙

(10)

Where: 𝑡𝑡𝑖𝑖 : Corona inception time 𝑡𝑡𝑠𝑠 : Time for streamers to cross the gap or meet the streamers from the opposite electrode 𝑡𝑡𝑙𝑙 : Leader propagation time

The corona inception time could be neglected without posing any problem considering the high rate of rise of the applied voltage; however, equation (11) shows the relation for streamer time. 1 𝐸𝐸 = 1.25 �𝐸𝐸 � − 0.95 50 ts

(11)

𝑢𝑢(𝑡𝑡) 𝑢𝑢(𝑡𝑡) 𝑑𝑑𝑑𝑑 = vl = 170. 𝐷𝐷. � − 𝐸𝐸0 � 𝑒𝑒 0.0015 𝐷𝐷 𝐷𝐷 − 𝑙𝑙 𝑑𝑑𝑑𝑑

(12)

𝑑𝑑𝑑𝑑 𝑢𝑢(𝑡𝑡) = k𝑢𝑢(𝑡𝑡) � − 𝐸𝐸0 � 𝑑𝑑𝑑𝑑 𝐷𝐷 − 𝑙𝑙

(13)

Where: 𝐸𝐸 and 𝐸𝐸50 are respectively maximum value of the average gradient reached in the gap before breakdown and 𝐸𝐸50 at 50% flashover voltage (𝑈𝑈50 ). Moreover, time for leader propagation is obtained by equation (12) [17].

Where: 𝑙𝑙 is the leader length (m), 𝑢𝑢(𝑡𝑡) is actual voltage (absolute value) in the gap and D is gap length. As it can be seen from the last equation, time for propagation is normally calculated by velocity which depends on the applied voltage and the leader length. However, with some practical simplifications [18], the following formula was introduced as a "best fit" to the volt-time curves for standard lightning impulses.

In Table IV, the practical parameters for different configurations and polarities are summarized. TABLE IV. PARAMETERS E AND K FOR DIFFERENT CONFIGURATION AND POLARITY [12]. configuration polarity k 𝑬𝑬𝟎𝟎 Air gaps, post and long rod insulators

+ -

Cap and pin insulators

+ -

0.8 . 10−6 1 . 10−6 1.2 . 10−6 1.2 . 10−6

600 670 520 600

V.

SIMULATION AND RESULTS

As it was mentioned previously, EMTP-RV software is employed in this paper to study the backflashover. Moreover, the components are accurately modeled in the software. The schematic of simulated line is shown in Figure7. It is necessary to note that for superposing the phase voltage on the induced surge voltage, each phase line should have an AC voltage source on both ends. Furthermore, Lightning current is injected into No.2 tower while two other towers are modeled to account for reflection of adjacent towers. The Convergence criteria are reached when PDF of rise and tail time of flashover current fit in their theoretical functions. With tradeoff between reaching convergence criteria with minimum error and the simulation time, 1000 random lightning current is selected. In order to generate the random variables in this paper, a program is written in MATLAB environment which generates 1000 random number according to their PDF. 52 lightning strokes to line per 100km per year is achieved based on doing number of flashes to the line per 100km per year calculations according to [6]. Indeed, with 1000 random lightning strokes, it can be claimed that the lightning performance of the TL is observed for approximately 40 years. Figure 8, Figure 9 and Figure 10 demonstrate statistical distribution of backflashover current rise time, tail time and current crest respectively. VI.

CONCLUSION

As mentioned earlier, the power system equipment failures can incur financial loss to transmission line owners. Therefore, the selection of optimum dielectric strength of the TL insulators plays a crucial role in minimizing these uncalled damages. This optimization process hinges on the deep insight of the harmful electrical transients including backflashover. In this paper, a probabilistic approach is employed to study the detrimental effect of backflashover on the insulators which leads to TL outages. From the simulation results, it has been found that 41 out of 1000 samples of random lightning strokes led to backflashover phenomena in upper phase insulator which means that 4.1 percent of lightning strokes can cause backflashover. Moreover, 2.1 line outage is achieved for 52 strokes in 100km per year which is 40 percent more than the outage rate calculated by conventional linear methods.

understanding of the backflashover. This knowledge can be utilized to get around varied problems posed by this phenomenon. REFERENCES

Figure 7

Figure 8

Simulated line schematic

Statistical distribution of flashover current rise time

Figure 9 Statistical distribution of flashover current tail time

Figure 10 Statistical distribution of flashover current amplitude

As Figure 8 and Figure 9 show that statistical distribution of backflashover current rise and tail time fit in log-normal probability function, the convergence criteria is met. In fact, applying more random data will lead to higher similarity between these graphs and the theoretical distribution, Figures. 1-2. As the current crest increases, the backflashover becomes more independent of the current waveshape. According to the calculations, after -110 kA, the dependence of the backflashover to the current waveshape becomes zero. For currents above this value, backflashover occurs regardless of the rise and tail time values. For the values lower than -110 kA, shorter rise time and longer tail time can cause backflashover at the lower current amplitude. The presented study as well as the obtained results could be used by power engineers to get a better

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