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This article presents a novel nonlinear coordinate damping controller (NCDC) for high‐voltage direct current (HVDC) and static var compensator (SVC) based on synergetic control theory, which can improve the stability of interarea power system and multi‐infeed HVDC system by quickly changing the transmission power of HVDC and reactive power of SVC. The traditional control design of HVDC and SVC can improve the stability, but there may be a negative interaction between the controllers of HVDC and HVDC or HVDC and SVC. Furthermore, the power system is a strong nonlinear system, and the controller designed by a linearized model may reduce its performance. To solve these problems, this article first constructs a unified macro variable and manifold, which contains the model of HVDC and SVC. The manifold sets the deviation value of the center of inertia (COI) frequency of the two systems connected by HVDC to zero. Then, a nonlinear HVDC and SVC coordinated controller is derived based on the synergetic control theory. The global stability of the controller is proven by the Lyapunov theorem. Finally, the simulation results in a two‐area power system and a multi‐infeed system using the power systems computer aided design (PSCAD) show the effectiveness and superiority of the proposed controller. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]