# Observations about Propagation, Attenuation, and Radiation of EMI from HVDC Converter Stations
## 3 Results  
### The Method of Moments: Attributes and Limitations  
One approach to modeling a substation, as suggested by CIGRE, is to use a large number of dipoles [1]. However, surfaces, such as the metallic shielding surfaces that surround a valve hall, are not readily modeled merely by dipoles. Given this, several authors have modeled substations using the method of moments (MoM), which provides a method for describing the electromagnetic fields of a collection of conductors with specified sources [12; 14; 15; 16; 17; 28; 29; 30]. The conductors are divided into small segments (effectively acting like dipoles) or surface patches (thus permitting the modeling of conducting enclosures such as those associated with a valve hall). The MoM is inherently a frequency-domain technique and thus the transient nature of the sources in an HVDC station must be accounted for by specifying the correct magnitude and phase of the spectral components of the excitation and transforming them to the time domain. The MoM does have several compelling attributes in terms of its modeling abilities. First, it permits the simple and accurate modeling of thin conductors such as those one would find throughout an HVDC converter station. Additionally, one can easily incorporate lumped elements at a point on a line or distribute a load over some portion of a line. However, caution must be exercised when modeling using a lumped circuit, since the modeling may require that the physical elements of the structure responsible for its lumped circuit behavior be eliminated. Finally, one need only determine the currents that flow on wires and surfaces. Once these are obtained, the fields can be obtained throughout the space. MoM was used by [PERSON] and [PERSON] [11] to show that it is critically important to create a full-wave model of the enclosure with the associated conductors passing through the shielding. As mentioned, they showed that there are situations in which the radiated field in a particular direction may be _enhanced_ because of the shielding enclosure [11]. As also mentioned, this contrasts, for example, with the statements in [5; 12] that indicate a valve hall provides at least 40 dB of reduced radiation. Again, the statements in [5; 12] are based on measurements and the authors do not provide a full-wave analysis of an electromagnetic environment representative of an actual valve hall. Because MoM has frequently been used to model emissions from converter stations, the authors decided to explore the degree to which the most recent version of the MoM-basedNEC code, i.e., NEC-5, could be expected to yield meaningful results for scenarios related to HVDC converter stations [24; 25]. More specifically, a simple test was created where a dipole source was enclosed in a simplified valve hall represented by a hollow metallic cube with 10 m sides. The dipole was aligned with the axes of the cube and centered in two of the dimensions but offset from the center by 3 m in one of the dimensions. The valve hall was \"perfect\", in that there were no holes in its walls nor conductors passing from the inside to the outside. The magnitude of the electric field was recorded over a circle that was 200 m in radius and centered about the \(z\) axis. If the numeric code was performing perfectly, the exterior fields would be identically zero at all points throughout the space exterior to the cube. However, that was not the result that was obtained. Since the MoM is a numerical method and the currents on the patches that represent the walls of the enclosure are discretized, the currents are always approximations and one would not expect perfect cancellation beyond the enclosure. Realistically, the best that one could hope for is that the exterior fields would be \"small\", but what constitutes \"small\", and the degree to which MoM can achieve that, appears open to question. In many applications, when comparing numerical results to either theoretical or measured results, an error of one percent is quite acceptable.