## XGSLabs Analysis Assumptions

### GSA and GSA_FD Modules

The following table summarizes the main assumptions on which GSA and GSA_FD module are based.

Aspects taken into account |
GSA |
GSA_FD |

Resistive coupling | Yes | Yes |

Capacitive coupling | No | Yes |

Self Impedance | No | Yes |

Mutual Impedance | No | Yes |

Soil parameters | ρ | ρ, ε = f(ω) |

Propagation law | 1/r | e-ϒr/r |

The following graph represents the application domain of the two modules. The highlighted area indicates the usual condition at power frequency.

The graph is obtained by a parametric analysis with a square meshed test grid energized with a current injected in a corner and made of copper. The analysed parameters were grid size “D”, soil resistivity “ρ” and frequency “f”. In its application dominion, the errors made by GSA in the GPR and touch voltages calculation are lower than 10%.

Application domain of GSA and GSA_FD

In practice, application limits of GSA and GSA_FD can be defined as a function of the wavelength of the electromagnetic field in the earth:

where:

λ (m) = wavelength

ρ (Ωm) = soil resistivity

f (Hz) = frequency

The previous graph indicates that GSA can be used if “D < λ/15”. GSA also requires “D < 500 m” because the effects of the DC component of the self impedance.

The parametric analysis is carried out assuming the test grid well meshed. The application limits about “D” may be lower than indicated if the grid shape is not regular, if the mesh are sparse and if the grid is made of steel.

The following figures show the surface potential obtained by applying GSA and GSA_FD to the same 100 m x 100 m grid as well as with the same injected current and injection point (marked with arrow) and the same soil model.

The qualitative difference between the results is also evident. GPR and impedance to earth tend to grow whether self impedance and mutual impedance are taken into account. High frequency or low soil resistivity or high impedance conductors (for instance steel conductors) can make this difference even more evident.

In brief, in grounding system analysis, at power frequency, GSA can be used in many practical situations but it tends to underestimate the results in case of low resistivity or large grids while GSA_FD may be applied in all cases.

At high frequency, GSA can be applied to grids with a maximum size of about some tens of meters. In general, at high frequency GSA_FD should be used.

In electromagnetic interference analysis, GSA and GSA_FD can be used respectively for only resistive and resistive + capacitive + inductive coupling evaluation.

After these conclusions a question could arise: Why not just GSA_FD?

GSA requires an easier data entry and fewer computer resources and, whenever applicable, it is the preferred module.

GSA_FD requires additional information about the topology of the conductor system and in order to calculate their self and mutual impedances and moreover a greater expertise in the evaluation of results.

If GSA cannot be used and calculation resources are not a limit, GSA_FD is the right solution.

### XGSA_FD and XGSA_TD Modules

XGSA_FD is based on a model similar to GSA_FD and takes into account the same aspects. Then the application limits of XGSA_FD for underground systems can be assumed as the same of GSA_FD while the application limits for overhead systems can be assumed from DC to a few MHz. XGSA_FD greatly expands the application field of XGSLab and it actually makes a real laboratory for engineering applications and for research.

XGSA_FD is an irreplaceable tool when the conductors network is partly overhead and partly underground. This situation is usual in electromagnetic fields evaluation (where sources may be underground cables or overhead wires) or interference analysis (where often the inductor is overhead and the induced is underground).

XGSA_FD is useful also for the evaluation of the fault current distribution. Furthermore, XGSA_FD may be used also in lightning design by using an equivalent single frequency sinusoidal input signal. For instance, the IEC 62305 standard first positive stroke T1/T2 = 10/350 µs can be simulated with a 25 kHz current, the first negative stroke 1/200 µs with a 250 kHz current and the subsequent stroke 0.25/100 µs with a 1 MHz current.

XGSA_TD can calculate the response in the time domain of a conductors network energized with a current or voltage transient. As known, the methods to calculate the transient behaviour of conductors network in the time domain can be divided into two main categories: those based on the calculation of the solution directly in the time domain and those based on frequency domain calculations and then using the forward and inverse Fourier transforms.

Methods of the first category require low frequency and quasi-static approximations and in addition do not allow considering the frequency dependent characteristics of the grounding system.

Methods of the second category use an electromagnetic field approach for the calculation of the response of the grounding system in a wide range of frequencies and have a good accuracy because they are based strictly on the principles of electromagnetism. On the other hand, in these methods, a system of equations has to be solved for every particular frequency, and a large number of discrete frequency points over the frequency band are chosen to satisfy the frequency sampling theorem.

XGSA_TD is based on the second category methods and uses XGSA_FD as solver in the frequency domain. Then the application limits of XGSA_TD can be assumed as the same of XGSA_FD and in particular the maximum bandwidth of the input transient should be lower than a few MHz.

This means that XGSA_TD can consider transient input as standard lightning currents. The lightning current can be simulated by using the following standard short stroke wave form IEC 62305: First positive; First negative; Subsequent negative.

With the direct Fourier transform the time domain input transient is decomposed in the frequency domain. In the following figures the normalized wave shape of the subsequent negative standard lightning current and their normalized frequency spectrum. The spectrum can be neglected when normalized values are lower than about 10-4. The standard lightning bandwidth is lower than a few MHz also for the most fast lighting, the subsequent negative ones.

Normalized frequency spectrum of subsequent negative standard lightning – Log-Log

After the calculation in the frequency domain (taking into account a reduced number of critical frequencies in order to limits the calculation time), the response in the time domain is obtained with the inverse Fourier transform.

The evaluation of lightning effects is important. For instance, current generated by a stroke flows in the LPS conductors and dissipate in the soil. The electric and magnetic field generated by such high voltages and currents may cause damage of equipment and may be dangerous for people.