Lightning performance of distribution lines: sensitivity to computational methods and to data

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1 Statistics, Sensitivity and Precision in Transient Analysis IEEE POWER ENGINEERING SOCIETY 200 WINTER MEETING Lightning performance of distribution lines: sensitivity to computational methods and to data Alberto Borghetti Carlo Alberto Nucci Mario Paolone Faculty of Engineering University of Bologna, Italy Columbus,Tuesday, January 30, 200 Outline of presentation. Introduction Sensitivity to data 4. Conclusions

2 Outline of presentation. Introduction Sensitivity to data 4. Conclusions Introduction Annual number of induced voltages exceeding the value in abscissa (or Annual number of flashover) LIGHTNING PERFORMANCE OF DISTRIBUTION LINE relevant to induced voltages VOLTAGE [kv] (or CFO) 2

3 Introduction The lightning performance assessment depends on: distribution of lightning parameters models used to calculate the induced voltages lateral distance expression line configuration Outline of presentation. Introduction Sensitivity to data 4. Conclusions 3

4 We shall compare IEEE Std Guide for improving the lightning performance of electric power overhead distribution lines proposed method the two methods differ in the computation of the induced voltages in the adopted statistical approach 4

5 IEEE Std distribution of lightning current parameters Anderson Transmission Line reference Book, 345 kv and above, Electric Power research Institute, ch. 2, 982 model used to calculate the induced voltages Rusck Trans. of the Royal Institute of Technology, Stockholm, No. 20, 958. lateral distance expression IEEE line configuration single-conductor line (plus sw) Distribution of lightning current amplitude IEEE: P( I I P * P ) = + * ( I / 3) 2. 6 P Cigré: I p 20kA I p = 6. ka δ ln Ip =.33 I p > 20 ka I p = 33.3 ka δ ln Ip = [ka] 5

6 Z Calculation of the Induced voltages: IEEE Rusck simplified formula U with max = Z o I P h + / d = / 4π µ / ε = 30Ω 2 v / v and h = line height t f = 0 (step function) v = return stroke velocity and v o = velocity of light d = distance of the stroke location from the line o 2 ( 0.5 ( v / v ) ) o which applies to infinitely long lines above perfectly conducting ground Lateral distance expression: IEEE y 2 2 min = rs ( rg h) r s =0 I 0.65 P r g =0.9 r s 6

7 Statistical approach: IEEE The range of lightning-peak current -200 ka is divided in intervals of ka The number of annual insulation flashovers per km of distribution line Fp is obtained as the summation of the contributions from all intervals considered as expressed by 200 i i Fp = 2 ( ymax ymin ) N g Pi i= * where Pi is the probability of current peak P( I P I P ) = * to be larger than Ip* + ( I / 3) 2. 6 y max is maximum distance range for every peak current interval at which lightning may produce an insulation flashover in the distribution line and is calculated using the Rusck formula for y by taking Ip* as the lower current limit of the interval and taking V max =.5 CFO. y min is the minimum distance for which lightning will not divert to the line and is calculated from the previously seen expression of the lateral distance. P Proposed method distribution of lightning current parameters Cigré R.B. Anderson, A.J. Eriksson, Lightning parameters for engineering applications, Electra, n. 69, pp , 980. model used to calculate the induced voltages those implemented in the LIOV CODE lateral distance expression IEEE, others line configuration single-conductor line, multi, 7

8 I p t f Correlation factor between t f and I P : 0.49 Probability Probabilità Cigré: t f = 3.83 µs δ ln t f = E-7.00E-6.00E-5.00E-4 Tempo alla cresta tf in s Front time [s] Calculation of the Induced voltages: proposed method Models LIOV code Return-stroke model: Modified Transmission Line LEMP: Uman and McLain and Cooray-Rubinstein Coupling model: Agrawal extended to the case of lossy ground This allows to take into account more realistic line configurations than the simplified Rusck expression 8

9 Statistical approach: proposed method Inputs: - lightning current parameters - return stroke velocity - line and ground data correlated 2 Random generation of events ( I p ; t f : x ; y) > Induced overvoltage calculation using LIOV 4 Counting of the events generating overvoltages greater than.5 x CFO 5 Plot the graph: No. of flashovers/00 km/year vs CFO where No. of flashovers/00 km/year = (n/n tot ) n g S 00/L (with n g =ground flash density) 9

10 Statistical approach: proposed method Why a striking area? Statistical approach: proposed method 0m lossy line A 50 m O' 5 km Induced overvoltages [kv] m 2500 m Time [µs] Details of the simulation. Lightning current amplitude = 2 ka Maximum rise time = 40 ka/us ground conductivity = 0.00 S/m 5000 m Line height = 0 m 0

11 Comparison We have first verified that our statistical method gives the same results of the IEEE method when the induced voltages are evaluated by using the Rusck formula instead of using LIOV, and when we assume the same distribution of the lightning current parameters, return-stroke velocity line height lateral distance expression and a perfectly conducting ground E+2 Comparison Flashovers/00km/yr for GFD= fl/km2/yr 0 0. IEEE Guide Proposed method In this simulation t f is log-normally distributed with a median value of 3.83 µs Correlation factor between t f and I P : CFO [kv]

12 Comparison The difference between our results and those of the IEEE Guide can be explained by observing that the simplified Rusck formula applies to the case of a step waveshape for the lightning current, while in the proposed method the current waveshape has a rise time t f different from zero and characterized by a certain statistical distribution (Cigré) We repeated our computation by keeping t f constant, and for different values of it Ideal ground E+2 Flashovers / 00 km / year 0 0. IEEE Guide LIOV - tf = 0.5 us LIOV - tf = us Note that with small values of t f the two methods predict basically the same results 0.0 LIOV - tf = 3 us CFO [kv] 2

13 Induced voltage [kv] LIOV - tf = 0.5 us LIOV - tf = us LIOV - tf = 3 us RUSCK Critical distance for Ip = 2 ka return stroke vel =.2 E8 m/s Distance [m] Outline of presentation. Introduction Sensitivity to data 4. Conclusions 3

14 Sensitivity to data Sensitivity to Ground resistivity Line configuration Sensitivity to ground conductivity E+2 Flashover / 00km / year IEEE Guide proposed method (ideal ground) proposed method (lossy ground) Ground conducitivity = 0.00 S/m CFO [kv] 4

15 Line configuration with shielding wire shielding wire phase conductor R t Z c R t R t R t Z c R t Hsw Line length = 2 km Influence of shielding wire height Annual no. of induced voltages with magnitude exceeding the value in abscissa / 00 km No. of induced voltages with magnitude exceeding the BIL /(00 km * year) phase conductor only 6 grs, Rt = 0 Ohm 6 grs, Hsw = 9.7 m, Rt = 0 Ohm 6 grs, Hsw = 0.4 m, Rt = 0 Ohm Basic Insulation Level [kv] 5

16 Influence of spacing between adjacent grounding Annual no. of induced voltages with magnitude exceeding the value in abscissa / 00 km No. of induced voltages with magnitude exceeding the BIL /(00 km * year) 00 phase conductor only 2 grs, Rt = 0 Ohm 0 3 grs, Rt = 0 Ohm 6 grs, Rt = 0 Ohm Basic Insulation Level [kv] Influence of grounding resistance Annual no. of induced voltages with magnitude exceeding the value in abscissa / 00 km No. of induced voltages with magnitude exceeding the BIL /(00 km * year) phase conductor only 6 grs, Rt = 0 Ohm 6 grs, Rt = 00 Ohm Basic Insulation Level [kv] 6

17 Conclusions. In this contribution we have described a statistical method to evaluate the lightning performance of a distribution line with respect to lightning induced voltages. 2. Such a method makes use of the LIOV code for the calculation of the lightning-induced voltages and of Monte Carlo based procedure. It provides a tool which allows to account also for lightning current parameters other than the peak value (e.g. the rise time), along with other important parameters, such as the ground resistivity. 3. Compared to method proposed in the IEEE Std Guide, it enables an improved assessment of the lightning performances of distribution lines. 7

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