1. Double space vector modulation and overmodulation of matrix converter were proposed in this paper to ensure the matrix converter switching frequency to be fixed and fast dynam-ic torque response.

2. In the overmodulation region, the new voltage vector's magnitude of strategy 2 is always larger than strategy 1's which leads to better dynamic performance.

3. The overmodulation algorithm is applied in the PMSM vector control system to increase output voltage of SVPWM inverter, and to extend the PMSM operation range.

4. In the condition of load reduction, overmodulation strategy 1 and 2 can quickly enter the stable state. However, overmodulation strategy 3 has a problem. The dynamic response time is very long.

5. After analysing the three existing overmodulation strategies, this paper perfects the overmodulation strategies and builds the overmodulation model of asynchronous motor vector control system.

6. The less switching loss mode and the overmodulation mode based on the proposed scheme are also presented.

7. To avoid an overmodulation problem in the flux-weakening region, the minimum distance overmodulation strategy is used.

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8. Overmodulation may be employed in the optical transmitter to increase the output power of laser diode.

9. In this paper, we propose two effective methods, namely the method of overmodulation and harmonic injection, to increase the voltage transfer ratio.

10. Moreover, the simulations and experiments of efficiency optimization control, as well as SVPWM overmodulation control, also verify that such IM model accords with the actual behaviors of IM.