# 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
Although this is a crude approximation of the electromagnetic behavior of the transformer at these frequencies, it is not an unreasonable one given the lack of a validated model of such a transformer in the open literature. Nevertheless, because of the shorting of the lines at this location, the model presented here could not predict the high-frequency currents on the AC lines exiting the AC yard. The conductors to the right (east) of the valve hall correspond to several of the lines that exist in the DC hall. The walls of the DC hall are not modeled. The 18 rectangular conductors seen within the valve hall serve as coarse approximations of the valves themselves. No attempt was made to model the detailed physical structure of the valves, but rather we modeled their overall size and shape to approximate how electromagnetic energy might propagate in their presence. A horizontal line passes through the center of each of the six sets of three \"valves\", moving from the AC to the DC side of the hall. Figure 1b shows a projection of the computational domain onto the \(xz\) plane while Figure 1c shows an oblique perspective projection of the computational domain. Energy is introduced into the computational domain by specifying the electric field at a particular FDTD node along one of the conductors. Specifically, the value of an \(E_{x}\) node along a line that transits from the AC to the DC side of the hall is specified by a source function at each time step of the simulation. This is the equivalent of specifying the voltage at that location. The source function was a unit-amplitude Ricker wavelet. (A Ricker wavelet is obtained by taking the second derivative of a Gaussian. In this way, the Ricker wavelet has somewhat similar spectral properties to a Gaussian pulse, but no DC component.) The Ricker wavelet had its peak spectral content at 10 MHz. This source  
Figure 1: Computational domain showing (**a**) a projection onto the \(xy\) plane, (**b**) projection onto the \(xz\) plane, and (**c**) an oblique perspective view. The red lines represent conductors, the shaded box corresponds to the valve hall, and the green-shaded plane on which the hall sits is a perfectly conducting ground plane. can be thought of as introducing energy over a range of frequencies that can be associated with commutation events. But, the simulations are performed with a single \"firing\" of the Ricker pulse at a single location. For this analysis, the source location is near the right edge of the center \"valve\" at the northern-most (greatest \(y\)) side of the valve hall, as shown in Figure 1a. Although the computational domain is finite, an infinite space is approximated by surrounding the computational domain with a perfectly matched convolutional layer [40]. Simulations were typically run for \(65,536\) time steps. Using the computational domain mentioned above (\(340\times 211\times 107\) cells), simulations took approximately one hour and \(49\) min to complete on Apple Mac Studio with an M1 Ultra processor and \(128\) GB of memory. For the discretization that was used, where the time step \(\Delta t\) was \(962.25\) ps, \(65,536\) time steps correspond to a total of \(63.06\)\(\upmu\)s. (The Courant number \(c\Delta t/\Delta s\) was the 3D limit of \(1/\sqrt{3}\).) In the FDTD method, boundary conditions at material interfaces \"take care of themselves\", as one merely specifies the material properties at all points throughout the discretized space, i.e., throughout the FDTD grid, and then advances in time via the discretized version of [PERSON]'s equations. However, perfect electric conductors (or nearly perfect conductors), such as those that pertain to the metal walls of a valve hall, are realized not by specifying material values per se, but rather by setting the electric fields tangential to such conductors to zero and leaving them at zero. (This is similar to the way in which conductors are realized, where a line of electric field nodes is set to zero.)