# 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
Simulations were performed of a perfectly intact valve hall where the conductors (red lines) shown in Figure 1 were present but terminated by unbroken conducting walls. The FDTD model of such an intact valve hall yields results consistent with our expectations: (1) In contrast to the MoM solution, the fields exterior to the hall are identically zero. (2) Once energy is introduced into the valve hall, either in the form of fields that radiate away from the source or currents induced on the line in which the source is embedded (and the fields associated with such currents), this energy simply oscillates inside the hall until the simulation is terminated. (3) Strong resonances occur owing to the structure of the hall and its associated interior conductors. When the model consists solely of perfectly conducting wires and walls, there is no loss mechanism and the fields resonate indefinitely in this rectangular cuboid. (The simulation does allow for \"loss\" in the form of radiation and subsequent absorption in the perfectly matched layer that surrounds the computational domain. However, such a loss can only take place if fields escape the valve hall. And, with the hall intact, no fields escape.) Nine holes were then introduced into the valve hall walls corresponding to the locations of each of the lines seen in Figure 1 that transitioned from the interior to the exterior of the valve hall (three on the AC side of the hall and six on the DC side). The size of the holes was not the minimum possible, but rather the minimum possible that would subsequently let us model a conductor passing through the hole. For the somewhat coarse discretization that was used (\(\Delta s=0.5\) m), the hole could be said to be approximately \(1\) m in diameter. Given that the peak spectrum of the pulsed excitation was at \(10\) MHz, i.e., a wavelength of \(30\) m, the holes were small compared to the wavelength of the bulk of the excitation. With the holes thus created, multiple simulations were performed with various modifications. First, in addition to introducing the holes, a \(2\) m section of each conductor passing through the walls was removed which was centered about the valve hall walls, i.e., a \(1\) m section of each conductor was removed to either side of the wall it passed through. Second, the conductors were left intact and merely passed through the holes. For both simulations, the magnitude of the electric field at two points was recorded, one point inside the hall and one point outside. These points were selected somewhat arbitrarily. Relative to the hole that was introduced to accommodate the northern-most line in Figure 1a, which passes from the valve hall to the DC hall, the \"inside point\" was \(4\) m away in \(x\) (i.e., \(4\) m further into the hall relative to the wall with the hole), \(3\) m away from the hole in \(y\) (\(3\) m closer to the center of the hall), and \(2\) m below the hole in the \(z\) direction. The outside point was \(4\)away in \(x\) (i.e., 4 m away from the wall), but, as with the inside point, 3 m away in \(y\) and 2 m away (below) in \(z\). Thus, each observation point was approximately 5.39 m away from the center of the hole. This northern-most line is also the one along which the commutation event is simulated. Figure 2a shows the field measured (for the remaining discussion of the results obtained via the FDTD method, measured and measurement should be considered synonyms for calculated and calculation) at the inside and outside points when the 2 m segments are removed from each line. The fields are plotted on a log scale over the first 5 us of the simulation. Note that the field inside the hall becomes non-zero prior to the field outside the hall due to its closer proximity to the source. The field inside the hall varies in the vicinity of roughly \(-45\) db, while the field outside the hall varies in the vicinity of roughly \(-95\) db, i.e., a reduction in the field of approximately 50 db.