An AC system’s voltage unbalance by a fundamental frequency negative sequence system is usually the main cause for the emission of non-characteristic harmonics by current source converters as used in conventional HVDC systems. This emission takes place on both sides of each 12-pulse converter. On the DC side mainly a 2nd harmonic voltage appears driving a 2nd harmonic current. The magnitude of this harmonic current can exceed the magnitudes of the characteristic harmonics even if no low order resonance exists. Further non-characteristic harmonics generated by the converter under such unbalanced supply voltage conditions have frequencies with a frequency distance to the characteristic harmonics of 2 times the fundamental frequency. The main technical drawbacks are the unintended coupling between both AC systems and the risk of thyristor over-stresses by DC current discontinuities at low power transfer levels. On both AC sides the largest 2 non-characteristic current harmonics generated by a 12-pulse HVDC converter under unbalanced supply voltage conditions are a negative sequence system of the fundamental harmonic and a positive sequence system of the 3rd harmonic. Also on the AC sides further harmonics are emitted by the converter with a order number distance of 2 to the orders of the characteristic harmonics. However, in practical AC system operation special attention has to be paid to the 3rd harmonic distortion level, in particular when low order resonance appears between the system impedance and the impedance of the converter station AC filters. In order to avoid the above mentioned problems, large smoothing reactors and sometimes large blocking filters are installed on the DC side and the voltage distortion on the AC sides is reduced by AC filters. However, these filters require an expensive high component rating if they are tuned to the 2nd or 3rd harmonic respectively. The work shows that a modification of the valve firing can reduce the levels of the 2nd and 3rd harmonic without investment into additional primary equipment. Furthermore, this offers the chance to reduce the minimum power transfer level since also the risk of an intermittent DC current can be reduced. A corresponding algorithm and a control strategy are proposed. However, the calculation of an appropriate firing pattern requires a detailed modelling of the processes within the converters, especially the formation of the harmonics and the harmonic transfer between AC and DC sides. The work proposes a component vector model for the calculation of the harmonics. This model assumes that each harmonic consists of a first component representing the ideal conversion process, a 2nd component representing the impact of different commutation angles and in the case of the modified firing a 3rd component considering the impact of the intended non-equidistant firing. The work shows, that the harmonic component vectors resulting from voltage unbalance and from firing modulation can be treated separately and superimposed linearly. The calculation of the harmonic component vectors is performed applying the method of switching functions. For the consideration of the commutation and firing angle differences the modelling of switching functions based on differential impulses is proposed. However, especially an accurate representation of the above mentioned 2nd component vector requires a correct calculation of the commutation angles and their valve-specific differences. The investigations of this work have revealed that the conventional method of calculating the commutation angles – assuming an ideal smoothed DC current - may not produce results of sufficient accuracy. This is especially true in the case of a high ripple of the DC current, e.g. smoothed with a small smoothing reactor. A small smoothing reactor is typical for HVDC back-to-back applications. Therefore a new analytical method for the calculation of the commutation angles has been developed which in particular considers the typical pulse form of the DC current and additionally the impacts of the voltage unbalance and of the proposed modification of the firing on the ripple shape of the DC current. Moreover, as this analytical method requires the instantaneous values of the DC current at the instants of valve firing, a further analytical method for the calculation of these discrete current values has been developed. The equations are valid under the same conditions as the new ones for calculation of the commutation angles, i.e. resistive-inductive AC system fundamental frequency impedances, any degree of DC current smoothing between ideal smoothing and a ripple at the limit for current discontinuities. Symmetrical conditions, supply voltage unbalances and non-equidistant firing as proposed are applied. It is shown that, using this method, also the discrete values of the DC current at the end of the commutation intervals can be determined. In practice one of these discrete current values indicates the minimum value during one period of the fundamental frequency. This offers the chance for a more exact analytical determination of the limit for the appearance of DC current discontinuities. For typical parameters of a back-to-back installation the new methods and the new analytical equations have been compared with simulation results showing excellent correlation for typical voltage unbalances of not more than 1...2% and firing angle differences of not more than 2.5°. This verification is performed for the harmonics, the commutation angles and the discrete values of the DC current at the firing instants as well.

An AC system’s voltage unbalance by a fundamental frequency negative sequence system is usually the main cause for the emission of non-characteristic harmonics by current source converters as used in conventional HVDC systems. This emission takes place on both sides of each 12-pulse converter. On the DC side mainly a 2nd harmonic voltage appears driving a 2nd harmonic current. The magnitude of this harmonic current can exceed the magnitudes of the characteristic harmonics even if no low order resonance exists. Further non-characteristic harmonics generated by the converter under such unbalanced supply voltage conditions have frequencies with a frequency distance to the characteristic harmonics of 2 times the fundamental frequency. The main technical drawbacks are the unintended coupling between both AC systems and the risk of thyristor over-stresses by DC current discontinuities at low power transfer levels. On both AC sides the largest 2 non-characteristic current harmonics generated by a 12-pulse HVDC converter under unbalanced supply voltage conditions are a negative sequence system of the fundamental harmonic and a positive sequence system of the 3rd harmonic. Also on the AC sides further harmonics are emitted by the converter with a order number distance of 2 to the orders of the characteristic harmonics. However, in practical AC system operation special attention has to be paid to the 3rd harmonic distortion level, in particular when low order resonance appears between the system impedance and the impedance of the converter station AC filters. In order to avoid the above mentioned problems, large smoothing reactors and sometimes large blocking filters are installed on the DC side and the voltage distortion on the AC sides is reduced by AC filters. However, these filters require an expensive high component rating if they are tuned to the 2nd or 3rd harmonic respectively. The work shows that a modification of the valve firing can reduce the levels of the 2nd and 3rd harmonic without investment into additional primary equipment. Furthermore, this offers the chance to reduce the minimum power transfer level since also the risk of an intermittent DC current can be reduced. A corresponding algorithm and a control strategy are proposed. However, the calculation of an appropriate firing pattern requires a detailed modelling of the processes within the converters, especially the formation of the harmonics and the harmonic transfer between AC and DC sides. The work proposes a component vector model for the calculation of the harmonics. This model assumes that each harmonic consists of a first component representing the ideal conversion process, a 2nd component representing the impact of different commutation angles and in the case of the modified firing a 3rd component considering the impact of the intended non-equidistant firing. The work shows, that the harmonic component vectors resulting from voltage unbalance and from firing modulation can be treated separately and superimposed linearly. The calculation of the harmonic component vectors is performed applying the method of switching functions. For the consideration of the commutation and firing angle differences the modelling of switching functions based on differential impulses is proposed. However, especially an accurate representation of the above mentioned 2nd component vector requires a correct calculation of the commutation angles and their valve-specific differences. The investigations of this work have revealed that the conventional method of calculating the commutation angles – assuming an ideal smoothed DC current - may not produce results of sufficient accuracy. This is especially true in the case of a high ripple of the DC current, e.g. smoothed with a small smoothing reactor. A small smoothing reactor is typical for HVDC back-to-back applications. Therefore a new analytical method for the calculation of the commutation angles has been developed which in particular considers the typical pulse form of the DC current and additionally the impacts of the voltage unbalance and of the proposed modification of the firing on the ripple shape of the DC current. Moreover, as this analytical method requires the instantaneous values of the DC current at the instants of valve firing, a further analytical method for the calculation of these discrete current values has been developed. The equations are valid under the same conditions as the new ones for calculation of the commutation angles, i.e. resistive-inductive AC system fundamental frequency impedances, any degree of DC current smoothing between ideal smoothing and a ripple at the limit for current discontinuities. Symmetrical conditions, supply voltage unbalances and non-equidistant firing as proposed are applied. It is shown that, using this method, also the discrete values of the DC current at the end of the commutation intervals can be determined. In practice one of these discrete current values indicates the minimum value during one period of the fundamental frequency. This offers the chance for a more exact analytical determination of the limit for the appearance of DC current discontinuities. For typical parameters of a back-to-back installation the new methods and the new analytical equations have been compared with simulation results showing excellent correlation for typical voltage unbalances of not more than 1...2% and firing angle differences of not more than 2.5°. This verification is performed for the harmonics, the commutation angles and the discrete values of the DC current at the firing instants as well.:1 Einleitung und Ziel der Arbeit 1.1 Einführung in die Problematik 1.2 HGÜ-Systeme als Quelle von Strom- und Spannungsharmonischen 1.3 Netzspannungsunsymmetrien 1.4 Abgrenzung der betrachteten technischen Systeme 1.5 Beweggründe für die Betrachtung 1.6 Zielstellungen 2 Erkenntnisstand und Analyse der Aufgabenstellung 2.1 Harmonische 2.2 Aktive Kompensation von Harmonischen 2.3 Diskrete Werte des Zwischenkreisstromes am Beginn und Ende der Kommutierungsintervalle 2.4 Kommutierungswinkel 3 Grundlagen 3.1 Methodischer Ansatz 3.2 Allgemeine Voraussetzungen, Annahmen und Festlegungen 3.3 Maßgebliche Impedanzen für die Stromaufteilung 3.4 Maßgebliche Impedanz für die gleichstromseitigen Stromharmonischen 3.5 Leerlauf-Klemmenspannung des Stromrichters 3.6 Kommutierungsspannung 3.7 Nummerierungssystem der Ventile 3.8 Überlappungsformen der Kommutierungsintervalle 3.9 Komplexer Spannungsunsymmetriefaktor 3.10 Anwendung und Modifikation von Schaltfunktionen 3.11 Verifikation der Ergebnisse 4 Harmonische auf der Gleichstromseite 4.1 Bildungsgesetz 4.2 Charakteristische Harmonische 4.3 Nichtcharakteristische Harmonische infolge unsymmetrischer Netzspannungen 4.4 Nichtcharakteristische Harmonische infolge Ansteuermodifikation 5 Diskreter Wert des Zwischenkreisstromes im Zündzeitpunkt 5.1 Vorgehensweise 5.2 Lösungsansatz 5.3 Konstante Gegenspannung 5.4 Reale Gegenspannung des HGÜ-Stromrichters 5.5 Berücksichtigung von Resistanzen 5.6 Unsymmetrische Netzspannungen 5.7 Ansteuermodifikation 5.8 Unsymmetrische Netzspannungen und gleichzeitige Ansteuermodifikation 5.9 Ergebnisse 6 Kommutierungswinkel 6.1 Vorgehensweise 6.2 Konstante Gegenspannung 6.3 Reale Gegenspannung des HGÜ-Stromrichters 6.4 Berücksichtigung von Resistanzen 6.5 Unsymmetrische Netzspannungen 6.6 Ansteuermodifikation 6.7 Unsymmetrische Netzspannungen und gleichzeitige Ansteuermodifikation 6.8 Ergebnisse 7 Vertiefende Betrachtung der nichtcharakteristischen Harmonischen auf der Gleichstromseite 7.1 Vorbemerkungen 7.2 Unsymmetrische Netzspannungen 7.3 Ansteuermodifikation 7.4 Spannungsunsymmetrie und gleichzeitige Ansteuermodifikation 7.5 Ergebnisse 8 Harmonische auf der Netzseite 8.1 Bildungsgesetz 8.2 Charakteristische Harmonische 8.3 Nichtcharakteristische Harmonische 9 Betrachtungen zur aktiven Kompensation 9.1 Vorbemerkungen 9.2 Betrachtungsumfang 9.3 Grundlagen 9.4 Konzeptioneller Vorschlag für die Kompensation der 2. Stromharmonischen 9.5 Betrachtung der Drehstromseite 9.6 Vorschlag zur Weiterentwicklung des Konzeptes 9.7 Berechnungsbeispiel zur Kompensation der 2. Harmonischen im Zwischenkreis 9.8 Ergebnisse und Schlussfolgerungen 10 Zusammenfassung 11 Literatur 12 Formelzeichen und Abkürzungen 13 Anlagenverzeichnis