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The paper is concerned with transient dynamics and stability of an electric power system with DC transmission. Nowadays, DC transmission systems are widely applied to conventional electric power systems. However, the transient dynamics of AC/DC power systems, affected by the active power that flows into DC transmissions, is not entirely understood. The paper derives a non-symmetrical swing equation system to analyse the transient dynamics of an AC/DC power system. The non-symmetry implies a unidirectional component of an external forcing that corresponds to both DC power and exciting power swing. The paper discusses a stability boundary and its qualitative change in the non-symmetrical swing equation system. An understanding of the stability boundary gives an important clue to the transient dynamics of AC/DC power systems. Fractal structure growth in the stability boundary caused by the change of DC power flow is described. The existence of a fractal boundary implies that the system behaviour becomes chaotic and unpredictable, depending on the operation of the DC transmission.