Analysis of harmonic cross-modulation in HVDC line-commutated converters for practical design purposes

Sammanfattning: The use of HVDC has many benefits over HVAC for some specific power transmission purposes. However, two major problems with HVDC links are that the converters produce harmonics and consume reactive power. Electrical filters are used to compensate for this and are a major cost driver of HVDC links. An accurate analysis of the modulation makes it possible to design an optimal filter solution in order to make the link financial viable. This report investigates how the complex cross-modulation phenomenon affects the harmonics. The investigation is limited to line-commutated converter technology (LCC) and excludes the newer voltage-source converter technology (VSC) for which the crossmodulation behavior is very different and requires completely different analysis techniques. This report refers to several MATLAB programs. All of these have been developed by the author as part of this thesis work. The report starts by explaining analytically, with the help of switching functions, how harmonics are cross-modulated across line-commutated converters. It is then explained and shown how a MATLAB program, BOWSER, in the time-domain can be used to calculate accurate switching functions when the converter is supplied with a general voltage source and when the DC current contains ripple. After that it is explained and shown how a second MATLAB program, DONKEYKONG, can be created to model an HVDC link in the frequency domain by iterating BOWSER. The cross-modulation phenomena is then finally analyzed in the frequency domain with the help of DONKEYKONG. The result is that the cross-modulation phenomenon can be divided into two groups, affected by grid and DC-side impedance as well as the overlap angle variation. Which will affect the characteristic and non-characteristic harmonics in different ways. It was found that the characteristic harmonics are affected by the cross-modulation due to grid and DC-side impedance by up to 12 % and that low order non-characteristic harmonics can diverge up to 900 % when the converter was supplied with 1 % fundamental unbalance. It also showed that the non-characteristic harmonics have almost the same amplitude for all power transmission levels of the HVDC link. The report shows that the cross-modulation caused by the grid and DC-side impedance, which is sometimes ignored or treated in a simplified way, can affect the practical filter design a lot. It also shows step by step how the MATLAB programs are created