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Improved electro‐geometric model for shielding failure analysis of transmission lines

2018; Institution of Engineering and Technology; Volume: 12; Issue: 4 Linguagem: Inglês

10.1049/iet-smt.2017.0423

1751-8830

Pejman Hashemian, Behrooz Vahidi, Abolfazl Rahiminezhad,

Lightning and Electromagnetic Phenomena

IET Science, Measurement & TechnologyVolume 12, Issue 4 p. 542-547 Research ArticleFree Access Improved electro-geometric model for shielding failure analysis of transmission lines Pejman Hashemian, Pejman Hashemian Department of Electrical Engineering, Amirkabir University of Technology, Tehran, IranSearch for more papers by this authorBehrooz Vahidi, Corresponding Author Behrooz Vahidi vahidi@aut.ac.ir orcid.org/0000-0002-9430-9468 Department of Electrical Engineering, Amirkabir University of Technology, Tehran, IranSearch for more papers by this authorAbolfazl Rahiminezhad, Abolfazl Rahiminezhad Department of Electrical and Computer Science, Esfarayen University of Technology, Esfarayen, North Khorasan, IranSearch for more papers by this author Pejman Hashemian, Pejman Hashemian Department of Electrical Engineering, Amirkabir University of Technology, Tehran, IranSearch for more papers by this authorBehrooz Vahidi, Corresponding Author Behrooz Vahidi vahidi@aut.ac.ir orcid.org/0000-0002-9430-9468 Department of Electrical Engineering, Amirkabir University of Technology, Tehran, IranSearch for more papers by this authorAbolfazl Rahiminezhad, Abolfazl Rahiminezhad Department of Electrical and Computer Science, Esfarayen University of Technology, Esfarayen, North Khorasan, IranSearch for more papers by this author First published: 01 July 2018 https://doi.org/10.1049/iet-smt.2017.0423Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract An improved electro-geometric model (EGM) based on upward corona leader system consideration is introduced. The proposed method is a modified version of EGM and its high accurate results are independent of the height, voltage level, and circuit type of structure. The equations of the proposed method are modified by means of genetic algorithm based on the leader progression models (LPM) results which are consistent with the experimental results. To evaluate the performance of the proposed method, the shielding failure rates (SFR) of a single-circuit transmission line with different protection angles are calculated and compared to those of LPM and a revised EGM. The comparisons show that the results of the improved method roughly agree with the results of LPM. To ensure about the performance of the proposed method, it is applied on ten different practical structures with different characteristics. The results of IEGM are compared to the field data and the results of the revised EGM. The comparisons demonstrate that the proposed IEGM is an appropriate method for SFR calculation irregardless of the height, voltage level, and circuit type. In other words, the proposed IEGM is as simple as conventional EGM and as accurate as LPM. 1 Introduction Transmission lines, as a vital component of power networks, have been exposed to natural disasters such as lightning, which may result in outages. Based on the reports of the State Grid Corporation of China (SGCC) and China Southern Power Grid (CSG), in roughly 98% of China power network, lightning is the main cause for the most of transmission lines unexpected outages [1, 2]. He et al. [2] statistically analysed the lightning activity in China and found that the total average lightning trip-out rate of 5 years reached ∼62% of the total transmission line trip-out faults. Therefore, protecting transmission lines against lightning is a key factor in transmission line design. Such designing requires highly accurate calculation of lightning strikes to the phase wires known as the shielding failure rate (SFR). Electro-geometric model (EGM) is the most widely used method for calculating the SFR and determining the shield angle of shield instruments [3]. The method was created by Young and improved gradually [4-6]. This method is based upon the striking distance as a function of lightning current [7]. Eriksson [8] found that the striking distance also depends on the height of earthed objects; thus, improved the method so that the height of the earthed objects is considered in the SFR calculation. However, the SFR predicted by EGM was associated with large errors, especially for the high-voltage structures [9]. Nevertheless, EGM is used wildly for SFR calculation because of its simplicity. In 1990s, Dellera and Garbagnati [10] and Rizk [11] introduced a new method for SFR calculation known as leader progression model (LPM) which is based on the physics of lightning. This method has been developed in the last years because of its highly accurate results [12-17]. Although the results of the SFR calculated by LPM have a high level of accuracy, it is a complicated and time-consuming method. Thus, engineers need a method which is both accurate and simple. Zhuang et al. [18] included the upward leader inception and its propagation angle to EGM for SFR calculation. This new modified EGM incorporates the physics of lightning into SFR calculation; thus, yields estimations that are closer to the field data. In that article, the formulation of upward leader and its propagation angle is calculated for the tower of a 1000 kV transmission line by means of numerical fitting of LPM results. Then, the effect of tower height is considered in the formulation. The paper showed that the estimations delivered by the revised EGM agree with those of LPM results. However, the LPM which the results are used for comparison neglects the space charge due to lightning's vertical movement, and zigzag movement of downward leader. Moreover, from [18], it can be concluded that the accuracy of the SFR estimated by the revised EGM decreased as the height of structures are changed. In this paper, the EGM model, which is modified by Zhuang et al., has been improved so that its estimations are highly accurate, irregardless of the structure characteristics. To achieve this, the revised EGM equations were modified so that the estimations delivered by improved EGM (IEGM) are coincident with those of LPM. It should be highly noted that the LPM presented in [12], in which the space charge and the zigzag movement of lightning downward leader are considered, is used for the results comparisons. The comparison of the results of the LPM to those of the actual observation at ten test towers [19] showed that the method is dependable. An evolutionary optimisation algorithm, i.e. genetic algorithm (GA) [20], is used to determine the coefficients of the equations of EGM in order to minimise the differences between the results delivered by the proposed IEGM and the LPM of [12]. The proposed IEGM is applied on different structures with different heights. The results demonstrate that the proposed IEGM has a good performance irregardless from the type, voltage level, and the height of structures. The rest of the paper is organised as follows: in Section 2, conventional EGM is briefly illustrated and its shortcomings are discussed. In this section, the revised EGM proposed by Zhuang et al. is also explained. In Section 3, the proposed IEGM is illustrated. Results and evaluation are in Section 4 and the conclusion is drawn in Section 5. 2 Conventional EGM and its shortcoming As mentioned before, EGM is the most commonly used method for SFR calculation and lightning protection system designing. In this method, for each object, a circular locus is defined. The object is considered to be struck by the lightning if the lightning enters to its locus. Shielding failure (SF) occurs when the lightning penetrates down to the locus of the phase wire. In the conventional EGM, the effect of upward leader is not considered. In fact, the EGM does not ignore the existence of the upward leader. However, it assumes that the upward leader mostly starts when the final jump condition is reached, and that the length of the upward leader in comparison to the final jump is insignificant. Nevertheless, the upward leader is a pivotal part of any lightning strike. Thus, failure to consider it makes the results unreliable, especially for high-voltage and ultra-high-voltage transmission lines situated at elevated towers. For instance, for a 60 m height communication tower, before final jump, an upward leader with the length of 65 m is recorded [21]. From the experimental results, it was concluded that the final jump occurred between the downward leader and the upward leader emanating from elevated objects [22]. Golde [23] stated that the necessary condition for striking of the downward leader was the inception of an upward leader from the elevated structures. Therefore, consideration of the upward leader before final jump is very important for lightning striking point determination. The main drawback of EGM is ignoring this important factor. Fig. 1 shows a comparison between the SFR calculated by EGM (based on the strike distance equations of Young, Brown–Whitehead, Mousa, Eriksson, and IEEE STD 1243), and LPM (the LPM illustrated in [12]) for a sample tower with the characteristics illustrated in [12]. As can be seen in Fig. 1, the EGM estimations are much lower than those of the LPM. In other words, the results of different models of EGM are so optimistic because they neglect the upward leader inception. Fig 1Open in figure viewerPowerPoint Comparison between predicted SFR with the LPM method proposed in [12] and conventional EGM with different striking distance equations 2.1 Revised EGM by Zhuang et al. [18] The experimental results show that the higher the operation voltage is, the faster and longer the upward leader of the structure would be [24-27]. Therefore, neglecting the upward leader by EGM leads to significant error in the results for SFR for high-voltage and ultra-high-voltage structures. To overcome this situation, Zhuang et al. modified the EGM in [18]. They considered the upward leader and its propagation angle in addition to the fundamentals of striking distance. By this idea, the EGM not only has the simplicity of the conventional EGM, but also models the physical behaviour of lightning. 2.2 Formulation In [18], the formulation of modified EGM is obtained by numerical fitting of the results of the LPM for a sample 1000 kV tower. Afterwards, the effect of the tower height is considered in the formulations. These formulas allow calculation of the leader's length, propagation angle of the leader, and striking distance for both shield wire and phase wire. These formulations are as follows [18]: The length of upward leader from the phase wire (1) The length of upward leader from the shield wire (2) The propagation angle of upward leader incepted from the phase wire (3) The propagation angle of upward leader incepted from the shield wire (4) Striking distance to the phase wire (5) Striking distance to the shield wire (6) Striking distance to the ground (7) where Ht is the height of tower, I the lightning current, Dc the unshielded area, Lup-c the length of upward leader from the phase wire, Lup-s the length of upward leader from the shield wire, θc the propagation angle of upward leader formed from the phase wire, θs the propagation angle of upward leader formed from the shield wire, Lc the striking distance to the phase wire, Ls the striking distance to the shield wire, and D the striking distance to the ground. It should be mentioned that in that paper, there is no mentioned that Ht is the height of phase wire or shield wire. 2.3 SFR calculation by means of revised EGM The SFR calculation principles of revised EGM are similar to those of conventional EGM which are based upon the striking distance. In the conventional EGM, the locus is drawn in the centre of the objects; while, in the revised EGM, the centre of the locus is the tip of the upward leader emanated from the objects. Therefore, the revised EGM equations which are used for obtaining the unshielded area (Dc) are different from the equations of conventional EGM, which are illustrated in the following paragraphs. Based on Fig. 2, using the EGM method, Dc can be calculated as follows: (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) Fig 2Open in figure viewerPowerPoint IEGM, definition of angles and distance (h, height of shield wire; y, height of phase wire; α, shield angle; Dc, unshielded area; Lup-c, length of upward leader from the phase wire; Lup-s, length of upward leader from the shield wire; θc, the propagation angle of upward leader incepted from the phase wire; θs, the propagation angle of upward leader incepted from the shield wire; Lc, striking distance to the phase wire; Ls, striking distance to the shield wire; D, striking distance to the ground) The equations for calculating the length and propagation angle of the upward leader ((1)–(7)) and Dc ((8)–(17)) for both phase wire and shield wire are more complicated in comparison to those of the common EGM. Therefore, calculation of Imax is not as simple as conventional EGM. Thus, numerical methods for calculating Imax are illustrated in the next part. 2.4 Calculation of Imax Fig. 3 represents the flowchart of Imax calculation procedure. In this method, the lightning current is increased by the step of 0.01 kA. In each step, the value of Dc is calculated based on (8)–(17). This process is continued until the value of Dc reaches a small value (for instance, <0.01). The lightning current corresponding to the smallest value of Dc is equal to Imax. Now, the SFR can be calculated as follows based on Dc and Imax [12]: (18) where γ is the lightning density in the unit of area in a year (flash/km2-year), and f(I) the probability density function of lightning peak current which is illustrated in details in [3]. Fig 3Open in figure viewerPowerPoint Procedure for calculating the Imax (I is the lightning current, Imax is the maximum lightning current, and Dc is the unshielded area) As mentioned, these formulas are obtained by numerical fitting of the results of the LPM. However, the LPM from which the results delivered does not consider the subject pockets of space charge which cause in vertical movement of the downward leader. Since the lightning has a zigzag motion, the foregoing LPM does not model the lightning with its physical behaviour. Thus, the results of the LPM and also the revised EGM cannot be dependable. 3 Proposed IEGM method 3.1 Bringing up an optimisation problem to improve the Zhuang et al. model As mentioned before, the results of the LPM illustrated in [12] agree roughly with the experimental results. Therefore, if EGM is modified, so that its results become close to the LPM, it can be an acceptable method for SFR calculation. In other words, such a method has not only the simplicity of the EGM, but also an acceptable level of accuracy. In this paper, an optimisation problem in which the objective function is to minimise the difference between the results of the IEGM and those of LPM is introduced. In other words, the EGM is improved so that the results of SFR for different values of lightning current will have the lowest difference with those of LPM introduced in [12], as the following presentation shows: (19) The main goal of this problem is to improve the revised EGM (the Zhuang et al. model), so that the results agree with the LPM results (introduced in [12]) for any height and structures. To minimise the foregoing objective function, an evolutionary optimisation algorithm, i.e. GA, is used. The equations proposed in [18] for (i) the propagation angle of the upward leader and its length, and (ii) the striking distance determination, for both phase wire and shield wire, are of the most important. The coefficients of these equations are considered as decision variables which should be determined optimally, in order to minimise the differences between the results of IEGM and those of LPM. These equations are defined as follows [18]: (20) (21) (22) (23) (24) (25) (26) (27) where m is the matrix of decision variables, and Y and H are the height of phase wire and shield wire, respectively. It should be mentioned that the coefficients of Ls and D are considered to be constant [4]. Moreover, the results of [18] demonstrated that the parameters Ls and D do not change with the variation of structure height; therefore, they are considered unique for any tower height. Meanwhile, parameter b in equation AIb is constant for any height [8]. The other point is that the parameter Ht in (1)–(7) is the height of the tower. In other words, the heights of the shield wire and also the phase wire are not taken into account; while, based on Eriksson's model, both the height of the phase and shield wires should be considered in [8]. In the equations used in this paper, the heights of both wires are considered. 3.2 Objective function The problem is to determine the coefficients of (27) optimally so that the SFR calculated by IEGM closely matches that of LPM. In other words, the parameters in (27) are optimisation variables and the difference between the SFR calculated by IEGM and the LPM (i.e. (28)) is the objective function. It should be mentioned that the results of dynamic simulations of lightning striking to the transmission line presented in [12] are considered as the desired value for the SFR which is the SFR of the protection system for Imin to Imax and for different protection angles and wire heights. In this paper, the SFR calculated for Imin, (Imax–Imin)/2, and Imax, for the height of 22.8, 27.8, 32.8, and 37.8 m, and the protection angles of 20°, 22°, and 26° are used for results comparison. Meanwhile, the 42.8 m height structure is considered for the evaluation of the proposed algorithm. The coefficients of (27) are optimally determined based on the SFR calculated by LPM method for the mentioned lightning currents, heights, and protection angles. Therefore, the objective function of this paper can be represented as follows: (28) where i denotes the phase wire height (1: 22.8, 2:27.8, 3:32.8, and 4:37.8 m), j the protection angle (1:20°, 2: 22°, and 3: 26°), and k the lightning current (1: Imin, 2: (Imax–Imin)/2, and 3: Imax). The objective function value reaches 0.054 in the optimisation procedure. It is obvious that the results of SFR calculated by proposed IEGM for these structures are roughly the same with those of LPM. The flowchart of solving the problem using the GA is shown in Fig. 4. Fig 4Open in figure viewerPowerPoint Flowchart of solving the optimisation problem 3.3 Optimal results The parameters used for GA are listed in Table 1. Using the optimisation algorithm and the aforementioned objective function, the optimal coefficients (matrix m) are determined and presented in Table 2. As said before, using these coefficients, the value of objective function reaches 0.054. In other words, a good curve fitting is done. Table 1. GA parameters GA parameters Value generation 200 population size 100 mutation 0.8 cross-over 0.8 type of cross-over one point type of mutation constant Table 2. Value of optimisation variables Parameter Value Parameter Value a 1.424 K 0.71 b −0.0115 M −0.285 c 0.86 N 0.009 d 4.244 P 1.15 e −0.0257 Q −0.667 f 0.56 S 0.0189 g 3.686 U 19.721 h −0.0215 T −13.479 As noted above, using (20)–(26) with the coefficients presented in Table 2, for SFR calculation, the lowest difference and thus the maximum compatibility between the results of LPM (presented in [12]) and the proposed IEGM are achieved. In other words, the results of the proposed IEGM are certainly better than the results of revised EGM proposed by Zhuang et al. for these structures. In order to evaluate the performance of the proposed IEGM, it is applied on a structure with the height of 42.8 m and four different protection angles. The results are compared with those of LPM and the revised EGM proposed by Zhuang et al. [18]. Moreover, to complete the evaluation of the proposed method, it is applied on ten different structures and the results are compared with the field data and the results of the Zhuang et al. model. 4 Results and evaluation To show how well the proposed IEGM performs, a single-circuit transmission line which the characteristics are explained in [12] is used as an evaluation criterion. Moreover, to evaluate the performance of the proposed method in SFR calculation, the proposed method is also applied on ten different practical structures which the detail of structures are explained in [20]. 4.1 Single-circuit transmission line The first structure with which the performance of proposed IEGM is evaluated is a single circuit transmission line. The dimensional characteristics of the structure are extracted from [12]. In this transmission line, the phase wire arrangement is horizontal. The height of structure is 42.8 m and the SFR calculated for four different protection angles including 18°, 20°, 22°, and 26°. As mentioned, the results of LPM are considered as the desired target. The SFR calculated by proposed IEGM are compared to those of LPM and the revised EGM proposed by Zhuang et al. in Fig. 5. As it can be seen, the results of proposed IEGM are nearly the same with those of LPM; while, the results of the revised EGM have a big difference compared to the LPM results (Fig. 5). In other words, the proposed IEGM has a worthy performance for the structure which is used for evaluation of the method. To ensure about the performance of the proposed IEGM, it is applied on some practical cases (Table 3) and the results are compared to the field data (Fig. 6). Fig 5Open in figure viewerPowerPoint Comparison between predicted SFR with the proposed IEGM, Zhuang et al. model, and LPM for shielding angle of (a) 18°, (b) 20°, (c) 22°, (d) 26° for a single circuit transmission line with the tower height of 42.8 m Table 3. Characteristics of different practical test cases Test cases CFO, kV Surge impedance, Ω Shielding angle, ° Td (days/year) Observed SFR (strokes/100 km-year) DU 30 1500 400 15 40 0.24 DU 39 1600 360 −15 40 0.19 DU 40 1580 400 14 32 0.07 DU 57 1470 360 20 78 0.77 DU 56 1470 360 20 98 0.84 DU 84 1610 400 18 31 0.4 DU 88 1800 450 20 16 0.08 DU 89 1800 450 20 22 0.17 500 kV — — −6.7 43 1.28 UHV — — −7 60.15 3.33 Fig 6Open in figure viewerPowerPoint Comparison between SFR obtained by Zhuang et al. model field observation and proposed IEGM 4.2 Discussion As mentioned before, EGM is a simple method which is widely used for SFR calculation. However, since this method does not consider the upward leader inception and its propagation before the final jump, its results are not coincident to the field observation. This issue intensifies as the voltage of under study structure increases. Thus, development of a more physical method was concerned by different researchers. In 1990s, Dellera and Garbagnati introduced a physical method known as LPM which is improved by many researchers such as Tavakoli [12]. Although LPM is an accurate method by which the SFR of different structures are obtained accurately, it is so complicated and time-consuming. Therefore, Zhuang et al. proposed a revised EGM in which the upward leader inception and propagation angle is taken into account. Nevertheless, the method is only appropriate for single-circuit transmission lines and limited to structures of specific heights. Thus, in this paper, an IEGM is proposed. The proposed method is a modification of revised EGM proposed by Zhuang et al., and the coefficients are optimally determined based on the results of LPM. Since the coefficients of proposed IEGM are based on LPM, it can be claimed that the proposed IEGM inherently considers the space charge and tortuosity of lightning. The proposed method is applied on a single transmission line structure and to obtain the SFR in different protection angle and the results are compared to those of revised EGM and LPM. The comparisons reveal that the results of the proposed IEGM are very close to those of LPM for different cases. Then after, the SFR of some practical structures (both single and double transmission lines structures) are calculated by the proposed IEGM and revised EGM and the results are compared to field observation. The comparisons show that the results of the proposed method are closer to actual data in comparison to revised EGM. Thus, it can be inferred that the proposed method can calculate the SFR of different structures with a high level of accuracy; while, the implementation is very simple and the results are obtained very fast. 5 Conclusion In this paper, EGM is improved using numerical analysis by the LPM results so that the upward leader and its propagation angle are considered, in addition to the striking distance principles. An improved version of LPM in which the space charge and the tortuosity of lightning is roughly modelled is used. By this idea, the proposed IEGM models the lightning closer to its physical process. The equations of upward leader inception from the phase and shield wires are presented, so that the results are nearly matched with those of LPM. To improve the EGM, an evolutionary optimisation algorithm, i.e. GA, is used. The objective function of the optimisation problem is minimisation of the differences between the SFR calculated by the proposed IEGM method and that of LPM. The optimisation variables are the coefficients of the equations proposed by Zhuang et al. To evaluate the performance of the proposed method, the results of SFR calculated by different methods for a single-circuit transmission line at 42.8 m heights and different protection angles are compared. The comparisons show that the Zhuang model [18] obtains higher SFR in comparison to those of LPM. On the contrary, the results of IEGM proposed in this paper agree roughly with those of LPM. To ensure about the worthy performance of the proposed method, it is applied on ten different structures with different heights, voltage levels, and circuit type. The results of the proposed IEGM are compared to those of the field data and LPM. The comparisons demonstrate the good performance of the proposed method. From the results it can also be concluded that the accuracy of the proposed IEGM method is independent of height or protection angle as well as circuit type, i.e. single- or double-circuit. 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Res., 2016, 130, pp. 103– 112 Citing Literature Volume12, Issue4July 2018Pages 542-547 FiguresReferencesRelatedInformation