Current control is an important topic in modern power electronics system. For voltage source inverters, current control loop ensures the waveform quality at steady state and the fast response at transient state. To improve the current control performance, quite a few nonlinear control strategies have been presented and one well-known strategy is the hysteresis current control. It achieves fast response without stability issue and it has high control precision. However, for voltage source inverter applications, hysteresis current control has a wide switching frequency range, which introduces additional switching loss and impacts the design of harmonic filter. Other nonlinear current control strategies include one-cycle control, non-linear carrier control, peak current control, charge control, and so on. However, these control strategies are just suitable for specific topologies and it cannot be directly used by voltage source inverters. The recently proposed parabolic current control solves the frequency variation problem of hysteresis current control by employing a pair of parabolic carriers as the control band. By the use of parabolic current control, approximate-constant switching frequency can be achieved. Due to the cycle-by-cycle control structure, it inherently has fast response speed and high precision. These advantages make it suitable for voltage source inverters, including stand-alone inverters, grid connected inverters, active power filters, and power factor correction applications. However, parabolic current control has some limitations, such as dead-time effects, only working as bipolar PWM, complex hardware implementation, non-ideal converging speed. These problems are respectively solved in this dissertation and solutions include dead-time compensation, the implementation on dual-carrier unipolar PWM, sensorless parabolic current control, single-step current control. With the proposed dead-time compensation strategy, current control precision is improved and stable duty-cycle range are extended. Dual-carrier PWM implementation of parabolic current control has smaller harmonic filter size and lower power loss. Sensorless parabolic current control decreases the cost of system and enhances the noise immunity capability. Single-step current control pushes the convergence speed to one switching operation with simple implementation. High switching frequency is allowed and power density can be improved. Detailed analysis, motivation and experimental verification of all these innovations are covered in this dissertation. In addition, the duality phenomenon exists in electrical circuits, such as Thevenin's theorem and Norton's theorem, capacitance and inductance. These associated pairs are called duals. The dual of parabolic current control is derived and named parabolic voltage control. Parabolic voltage control solves the audible noise problem of burst mode power converters and maintains high efficiency in the designed boost converter. / Ph. D. / Current control strategy is an important topic in power converter design. Good current control strategy helps to control the quality of input or output waveform of power conversion systems. This dissertation studied an attractive current control strategy named parabolic current control. Parabolic current control solves some drawbacks of conventional current control strategies with enhanced performance. However, it still has some application limitations. This dissertation proposed four new strategies to solve the application limitations of parabolic current control. Motivated by the duality phenomenon, a voltage control strategy named parabolic voltage control is also proposed, serving as the dual of parabolic current control. By the use of parabolic voltage control, audible noise in some power conversion systems can be eliminated and conversion efficiency can be ensured. All these new ideas in this dissertation are carefully derived in theory and verified by experimental test results.