I. Introduction
High voltage direct current (HVDC) transmission has advantageous performances in long-distance bulk-power delivery, interconnection of two asynchronous power systems, underground and submarine cable transmission, multiterminal system applications, and so forth [1], [2]. However, due to the nonlinearity of the power converters, HVDC system causes harmonic problems to the power networks to which it is connected and itself [3], [4] . In most line-commuted converter (LCC) HVDC systems the 12-pulse converters are utilized to reduce the harmonics in 6-pulse operation [1], [5] , in terms of complexity and economy [6]. However, the 12-pulse operation is still not perfect enough to keep the ac power grid from harmonic pollution. Consequently, harmonic filters for 11th, 13th and higher-order harmonics and power factor correction capacitor banks are necessary to improve the power quality of the power grids and compensate the reactive power consumed by the converters. In traditional LCC HVDC systems, the harmonic filters and compensating capacitors are generally installed at the ac grid side. In this way, the power quality of ac networks can be improved effectively. Nevertheless, with respect to the converter transformers which are the most important electromagnetic equipments in a HVDC system, the harmonic currents still penetrate them inevitably [1], [6]– [8]. As a result, the detrimental effects caused by harmonics on the converter transformers are unavoidable, including capacity derating, increase in power losses, temperature rise, vibration and noise, and operating cost, decrease in efficiency, insulation strength and service life, and so forth [5], [10]– [18].