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Power injection variations that occur in power systems are generally nonlinear. A continuation power flow method with multiple nonlinear power injection variations is presented in this paper. To model the nature of nonlinear power injection variations, a piecewise-linear model is proposed to approximate the nonlinear model of power injections. The piecewise-linear model is studied and incorporated into continuation power flow, making it capable of handling nonlinear power injection variations. The impacts of linear as well as nonlinear load variations on the P-V curve, Q-V curve, and P-Q-V curve are numerically analyzed on test power systems. Numerical studies indicate that the direction of power injection variation can significantly affect the load margin and that the differences between uniform linear power injection directions and multiple nonlinear power injection variations can be significant. The importance of accurately modeling power injection variations on simulated power system quasi-state behaviors is stressed.