Smart Grids and Micro-Grids. Umashankar Subramaniam

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Smart Grids and Micro-Grids - Umashankar Subramaniam


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target="_blank" rel="nofollow" href="#ulink_a64b0abf-514c-5172-bf3c-a3a012434954">Figure 2.3 Typical configuration of the controller.

       2.5.1.1 Modeling and Control of the Converter

      The instantaneous state-space variable vector can be written as,

Schematic illustration of the equivalent circuit of the converter.

      (2.3)image

      The current compensator is given by

      (2.4)image

      Where kp, i and ki, i are gain of PI controller of current loop. The control system loop gain is

      (2.5)image

      For improving the open-loop frequency response, the pole can be canceled by the zero of the PI compensator. Defining τi is the desired time constant of the closed-loop system (image is the bandwidth of the current closed-loop), we can choose

      (2.6)image

      (2.7)image

      As discussed earlier, sometimes the dc-dc converter is supposed to control the output voltage, i.e., dc microgrid voltage. To derive the transfer function between the output voltage and inductor current which would be the outer control loop of the converter, let the perturbation in output voltage be image. Using the perturbations in equation (2.1) and linearizing the resulting expressing, one would obtain

      (2.8)image

      (2.9)image

      The voltage compensator is given by

      (2.10)image

      Where kp,v and ki,v are gain of PI controller of voltage loop. The control system loop gain is

      (2.11)image

      As stated earlier, the pole can be eleminated by the zero of the PI compensator. Defining τv is the desired time constant of the closed-loop system (image is the bandwidth of the voltage closed loop), we can choose

      (2.12)image

      (2.13)image

       2.5.1.2 Typical Case Study in MATLAB-Simulink

      (2.14)image

      (2.15)image

      (2.16)image


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