# Observations about Propagation, Attenuation, and Radiation of EMI from HVDC Converter Stations
## 3 Results
### The Finite-Difference Time-Domain Method: Initial Insights from Simple Geometries  
The finite-difference time-domain (FDTD) method [31; 32] employs a fundamentally different approach. One must discretize not only the sources themselves, but also the space in the vicinity of the sources and the space that surrounds any physical features that might affect the field of interest. In addition to discretizing space (where the discretization assigns the appropriate material properties to each point in the discretization), the FDTD method also discretizes time. In this way, all the derivatives in Maxwell's equations (specifically the curl equations) are replaced with central differences. This yields a set of equations where future (unknown) fields are expressed in terms of past (known) fields. One then advances by incremental steps in time, revealing the time-domain behavior of the fields. While the MoM is a frequency-domain technique that allows one to obtain fields throughout space at a single frequency, the FDTD method is a time-domain technique that can potentially yield results over a broad spectrum with a single simulation. However, the FDTD method will only directly yield the fields within the space that has been discretized. If one is interested in fields outside of the discretized space, one must carry out a transformation of the known fields to the point of interest. The FDTD method is generally considered to be quite computationally demanding. Furthermore, special consideration is needed to handle any number of features of a particular scenario, such as a relevant physical structure that is small compared to the discretization that is used. Several FDTD simulations were run using code developed in-house that explored various aspects of HVDC converter station modeling with an emphasis on the effect of the valve hall. The first considered was a \"perfect\" valve hall. As with the initial MoM testing, this hall had no openings or any conductors running from the interior to the exterior. However, instead of using a cube with 10 m sides, the dimensions were based on those of an actual converter station. The valve hall dimensions were (\(x\)) 42 m by (\(y\)) 68 m by (\(z\)) 19 m. The hall and surrounding space were discretized with a step size \(\Delta s\) of 0.5 m. Initial simulations, which incorporated part of the AC yard and the DC hall (reactor hall), used a computational domain of \(340\times 211\times 107\) cells in the \(x\), \(y\), and \(z\) directions, respectively. The computational domain is depicted in Figure 1, where the scale is in terms of FDTD cells (one can divide by two to convert to meters). Red lines correspond to conductors and the rectangular structure near the center of the figures corresponds to the valve hall. Conductors are modeled as a line of electric field nodes set to zero. Several researchers have reported that the \"effective\" radius \(r_{0}\) of such a line of cells is approximately 0.2\(\Delta s\)[33; 34; 35; 36; 37], ranging from 0.135\(\Delta s\)[33] to 0.23\(\Delta s\)[35]. In [33; 36; 37; 35], the researchers proposed ways to modify the FDTD update equations to model wires that had radii that were either smaller or larger than this effective radius. In [38], [PERSON] et al. reexamined the effective radius in the context of surge impedance and compared FDTD results to the theoretical work of [PERSON] [39]. They obtained an effective radius of \(r_{0}=0.199\Delta s\). This is taken to be the most accurate value of the effective radius. Applying that to the modeling performed here yields an effective conductor radius of roughly 10 cm. The green plane on which the valve hall sits is a perfectly conducting ground plane. Figure 1a shows its projection onto the \(xy\) plane (the green ground plane has been removed from this view). The AC yard is to the left (west) of the valve hall. The three lines in the AC yard ultimately are shorted together at what would be, in practice, the location of a transformer.