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An Accurate Method of Determining Conductor Short Circuit Withstand Capability Lucas Cook, P.E. 2021 IEEE Power & Energy Society General Meeting (PESGM) | 978-1-6654-0507-2/21/$31.00 ©2021 IEEE | DOI: 10.1109/PESGM46819.2021.9638243 NEI Electric Power Engineering Inc. Lakewood, CO USA lcook@neieng.com When designing a wind or solar plant collection system, it is important to verify that the cable conductors and concentric neutrals can withstand the worst-case short circuit event during the life of the project. Existing standards provide equations for calculating the withstand capabilities of these conductors. However, these standards provide no guidance on what current value should be used in these equations. It will be shown that two commonly used methods are inaccurate, with one being overly conservative, and one being insufficient. An accurate method of determining the correct current value will be presented. The impacts to the cable sizing of two representative projects will be explored for all three methods. It will be shown that the accurate method prevents unnecessary cable up-sizing compared to the overly conservative method but causes additional cable up-sizing compared to the insufficient method. To conclude this paper, it is suggested that the new method be incorporated into the relevant standards to provide clarity to practicing engineers and to ensure that cables are properly sized in any underground cable installation. experience temperatures higher than their rating. In the United States, there are a few standards which the industry relies upon to perform these calculations. However, these standards make no mention of which current value needs to be considered. An engineer may run a short circuit analysis using a power system modelling software, but have a difficult time determining which current to use in the calculation (e.g. symmetrical, asymmetrical ½-cycle, etc.) Index Terms—Asymmetrical current, Cable, Collection System, Concentric Neutral, DC Offset, Distribution, Renewable, Short Circuit, Solar, Underground, Wind, Withstand, X/R In addition, the three different calculation methods and their impacts to final cable sizes will be compared so that any renewable energy project stakeholder may understand the impacts of the computational methods being used by their engineer. I. INTRODUCTION When designing an underground medium voltage (MV) collection system for a wind or solar project, the engineer must consider the ability of the underground cables to withstand the worst-case short circuit event. Underground cable installations are relatively expensive compared to overhead installations. A renewable energy project owner will expect to reliably operate the project for 20+ years. Reducing the possibility of cable failures and the associated capital expense during the life of a project is the main benefit to proper cable sizing. The possibility of re-using existing underground collection systems for future repower efforts makes it even more important to size cables properly from the start. During a short circuit event, it is possible that the MV cable conductor and concentric neutrals, as well as any trench grounding conductors will be subjected to high amounts of short circuit current. The goal of a short circuit withstand analysis is to verify that the cable and its components will not This paper will contemplate two simple methods that engineers are currently using (one overly conservative, and one overly aggressive). A new, accurate method will be presented to calculate an equivalent current for use in the short circuit withstand calculation. The key feature of this equivalent current is that it accurately accounts for the DC offset (X/R ratio) of a fault current without being overly conservative. The equation to calculate this equivalent current has been derived and can be easily implemented by anyone performing these calculations. II. EXISTING CALCULATION METHODS A. Conductor Withstand In a typical short circuit study, the withstand capability of the main conductor of the cable is verified using the following equation from page 9 of ICEA P-32-382. The variable “I” is labeled simply as the “Short Circuit Current – Amperes” [1]. (1) B. Concentric Neutral Withstand The concentric neutral short circuit withstand is determined using an equation from ICEA P-45-482, shown Authorized licensed use limited to: Universidade Tecnologica 978-1-6654-0507-2/21/$31.00 ©2021 IEEEFederal do Parana. Downloaded on December 13,2023 at 16:49:39 UTC from IEEE Xplore. Restrictions apply. below. The variable for current is labeled as “short-circuit current, ampere” [2]. (2) C. Application of Existing Equations Selecting the fault currents to use in the above equations seems to be left to the discretion of the engineer. Leaving the selection of fault current open to interpretation may lead to confusion, since there are several fault current choices such as symmetrical, ½-cycle asymmetrical, peak asymmetrical, etc. If an engineer chooses the symmetrical fault current, he will not properly account for the system’s X/R ratio. Large X/R ratios may be present on wind and solar projects due to the often-large main power transformers (MPT’s) used at the project substations. The remainder of this paper will propose a correct method to perform this short circuit analysis and compare the impacts of the various approaches. III. DERIVATION OF AN EQUIVALENT CURRENT To properly account for the DC offset of a fault current, it must first be recognized how the fault current mathematically adds heat to the cable. The key quantity in an energy absorption problem is the square of the current multiplied by time (I2t). Examining the power equation clarifies this (P = I2R). Multiplying this expression by time will provide energy. Hence, energy absorption is proportional to I2t. This derivation also requires an equation of the total (asymmetrical) fault current (from basic circuits theory). That equation is shown below. (3) The approach for deriving an equivalent current will be to integrate the square of equation (3) from a time of 0 seconds (start of the fault) to an arbitrary clearing time (t), set that expression equal to an equivalent current squared multiplied by time (Ieq2t), and solving for the equivalent current. Squaring equation (3) and rewriting as a function of time (t) yields the following expression. (4) The following equations show the result of the integration and solving for the equivalent current. (5) (6) (7) Equation (7) is the final expression for an equivalent current. This equation may be used to determine the current values to use in the ICEA equations. This equation will allow an engineer to accurately determine the impacts of DC offset with the greatest amount of accuracy. For avoidance of doubt, the proposed methodology is to use RMS current values in these equations. RMS values are representative of the actual energy absorbed in any situation. IV. IMPACT TO A PROJECT’S CAPITAL EXPENSE Two sample wind projects (A and B) of approximately 300 MW consisting of 12 (twelve) underground 34.5 kV feeders were considered. The final cable short-circuit sizing was completed using three different fault currents: • Symmetrical • ½-Cycle Asymmetrical • Equivalent (see section III) The impacts to cable sizes and quantities is the focus of this analysis. A base cable bill of materials (BOM) is established based on ampacity only and shall serve as the starting point for each case. The short circuit withstand of all cables is iteratively verified, upsized, re-verified, and upsized again until there are no short circuit withstand violations. The key design parameters of the system are listed below: • • Two (2) MPT’s per Project: o Project A: 105/140/175 Impedance, X/R = 52 MVA, 10% o Project B: 105/140/175 Impedance, X/R = 49 MVA, 9.5% The following possible cable sizes: o 1/0 AWG, 2/3 Neutral o 4/0 AWG, 1/2 Neutral o 500 kcmil, 1/3 Neutral o 1000 kcmil, 1/8 Neutral o 1250 kcmil, 1/8 Neutral Authorized licensed use limited to: Universidade Tecnologica Federal do Parana. Downloaded on December 13,2023 at 16:49:39 UTC from IEEE Xplore. Restrictions apply. o 1500 kcmil, 1/8 Neutral • Clearing time for ground and phase faults: 10 cycles • Concentric Neutral Split Factor: 70% • Utility Fault Current (at 345 kV): o Project A: 7 kA o Project B: 11.5 kA B. Project B Results Tables 3 and 4 below display the same data for Project B. A. Project A Results As shown in Table 1 below, considering short circuit withstand beyond the base case results in a substantial difference in cable quantities. This should reinforce the fact that short circuit withstand needs to be considered as part of a prudent collection system design. Table 1 – Project A Cable Quantities in Feet Cable Size 1500 kcmil 1250 kcmil 1000 kcmil 500 kcmil 4/0 AWG 1/0 AWG method results in approximately 20,000 feet of additional cable upsizing compared to the symmetrical current method. This confirms that using the symmetrical current without regards to DC offset can lead to undersized cables. Table 3 – Project B Cable Quantities in Feet Cable Size 1500 kcmil 1250 kcmil 1000 kcmil 500 kcmil 4/0 AWG 1/0 AWG Base Asym. Sym. Eq. 219,381 219,381 219,381 219,381 281,550 303,582 281,550 281,550 474,204 452,172 474,204 474,204 278,889 281,778 278,889 278,889 124,353 336,510 224,331 243,378 Cable Size 510,915 295,869 410,937 391,890 1500 kcmil 1250 kcmil Table 2 – Project A Cable Quantity Differences in Feet 500 kcmil 1500 kcmil 1250 kcmil 1000 kcmil 500 kcmil 4/0 AWG 1/0 AWG 1000 kcmil Eq. – Sym. Eq. – Asym. Eq. – Base 4/0 AWG - - - 1/0 AWG - (22,032) - - 22,032 - - (2,889) - 19,047 (93,132) 119,025 (19,047) 96,021 (119,025) As shown in Table 2, the asymmetrical current method results in substantially more cable upsizing than the equivalent method, confirming that using the asymmetrical current is overly conservative. In addition, the equivalent Asym. Sym. Eq. 230,451 230,451 230,451 230,451 225,258 267,699 225,258 225,258 368,565 326,124 368,565 368,565 200,913 264,918 200,913 220,035 89,457 255,618 233,613 243,096 358,755 128,589 214,599 185,994 Table 4 – Project B Cable Quantity Differences in Feet Conclusions are best drawn by comparing the difference in cable quantities between the equivalent current method and the other methods. See Table 2 below. Cable Size Base Eq. – Sym. Eq. – Asym. Eq. – Base - - - - (42,441) - - 42,441 - 19,122 (44,883) 19,122 9,483 (12,522) 153,639 (28,605) 57,405 (172,761) As shown in Table 4, the asymmetrical method once again results in more cable upsizing compared to the equivalent current method. The equivalent current method results in approximately 29,000 feet of additional cable upsizing compared to the symmetrical current method, further reinforcing the point that DC offset must be considered. Only two projects have been considered in this analysis. The key result is that 20,000-30,000 feet of larger cable was required when using the equivalent current method as opposed to the symmetrical current method. The typical cable sizes that require upsizing are 1/0 and 4/0. If another project has a particularly large amount of 1/0 and 4/0 cable runs, the impact of the DC offset on cable quantities may be even greater. Conversely, projects that have very few 1/0 Authorized licensed use limited to: Universidade Tecnologica Federal do Parana. Downloaded on December 13,2023 at 16:49:39 UTC from IEEE Xplore. Restrictions apply. and 4/0 cable runs may not be as impacted by adopting the equivalent current method. Due to the mathematical impact that X/R has on the equivalent current method, it is expected that larger system X/R ratios will result in the need for additional cable upsizing when using the equivalent current method. V. CONCLUSION It should be emphasized that only two possible collection system topologies and one design basis have been considered in this paper. Although this set of assumptions is considered by the author to be typical and representative of most wind projects, the impacts of the different calculation methods on a project may vary. Regardless of the actual system under consideration, it is proposed that equation (7) always be used for these calculations to provide an accurate assessment of the fault current that a conductor may experience. Engineers often use overly conservative calculation methods to account for unknown variables that they may have not accounted for. Continuing to use the asymmetrical fault current method, while technically overly conservative, may be a valid way of account for some uncertainty in the calculation (e.g. fault current duration). However, if an engineer wishes to perform the short circuit withstand as accurately as possible, equation (7) offers him this ability. Finally, using the symmetrical fault current no longer appears to be a valid approach, as the X/R of the system will impact the cable’s ability to withstand a short circuit event. REFERENCES [1] [2] ICEA Short Circuit Characteristics of Insulated Cables, ICEA Std. P32-382, February 2013 ICEA Short Circuit Performance of Metallic Shields and Sheaths on Insulated Cable, ICEA Std. P-45-482, February 2013 Authorized licensed use limited to: Universidade Tecnologica Federal do Parana. Downloaded on December 13,2023 at 16:49:39 UTC from IEEE Xplore. Restrictions apply.