**The following updates and improvements have been recently implemented for cyclic loading calculations: The load factor was limited to values of above 0.5, the influence of mutual heating from other cable systems has been modified, and a new method to consider cyclic loading from Heinhold has been added.**

Posted on April 12, 2019

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There are different analytic approaches considering the cyclic loading pattern of a cable system. Neher/McGrath [1, 2] offered a method for considering cyclic loading by making an assumption that the 24-hour load cycle closely followed a sinusoidal load shape. On this basis, peak losses are applied to cable components and the portion of the earth thermal circuit that is “near” to the cable, while average daily (24-hour cycle) losses are applied to the thermal resistance values of the ground beyond a characteristic diameter. This method is only applicable for a load factor (LF) down to 0.5. This limitation is specified in a Siemens handbook (Heinhold 1999) and does also apply to the methods by Neher/McGrath and Dorison [3].

When there are multiple cable systems in parallel, mutual heating between them must be considered. The temperature rise $\Delta \theta_{kp}$ of cable $p$ is caused by the losses from cable $k$. The losses from cable k are multiplied by the loss factor $\mu$ (which is < 1) if the distance between the two cables (= the soil between the cables) is greater than the calculated characteristic diameter $D_x$.

Previously, we did not multiply the losses of cable $k$ with $\mu$ when calculating the mutual heating in order to be on the safe side in case the cables are located closer than $D_x$. Otherwise, the results would have been far too optimistic for cables located close to other cable systems. But because this was rather pessimistic, we allowed for an $LF$ down to 0.3.

With the latest update, we now check the distance between each object and consider $\mu$ individually depending on the distance. If the distance is smaller than $D_x$, the losses will be increased linearly with a factor from $\mu$ to 1 over the distance between $D_x$ and the cable diameter $D_e$. But we do no longer allow for an $LF$ < 0.5 because this could potentially be too optimistic.

At the same time, we introduced a new method to consider cyclic loading from Heinhold (1999) [4]. With this method, one can select sinusoidal, rectilinear and mixed load shapes. The methods by Neher/McGrath and Dorison all consider sinusoidal load shapes. For example, the load shape of a PV power plant is closer to a rectilinear shape than to a sinusoidal shape.

[1] | J. H. Neher, "Procedures for Calculating the Temperature Rise of Pipe Cable and Buried Cables for Sinusoidal and Rectangular Loss Cycles", 1953 |

[2] | J. H. Neher, M. H. McGrath, "The Calculation of the Temperature Rise and Load Capability of Cable Systems", 1957 |

[4] | E. Dorison et. al., "Ampacity Calculations for Deeply Installed Cables", 2010 |

[4] | L. Heinhold, R. Stubbe, "Kabel und Leitungen für Starkstrom. Grundlagen und Produkt-Know-how für das Projektieren von Kabelanlagen", 1999 |

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