Page 121 - Uninterruptible Power Supplies
P. 121

Harmonic Distortion of the Supply
                                             Harmonic Distortion of the Supply  119


              Conventionally, nonlinear loads are regarded as loads which take
            current at the fundamental frequency and which include, in series,
            harmonic current generators having zero impedance.
              There are a number of formulae likely to be encountered in connection
            with nonlinear loads; they appear below and use the following convention:

              a   rms value of the total current
              a 1   rms value of the fundamental current component
              a n   rms value of the nth harmonic current component
            The rms value of total current   a
                                           a   a    a    a  …           (4.1)
                                              2
                                                   2
                                                       2
                                                            2
                                              1    2   3    4
                                rms value of the fundamental current component
            Distortion factor
                                         rms value of the total current
                                          a 1
                                                                        (4.2)
                                 a   a    a    a
                                                  2 …
                                             2
                                    2
                                        2
                                    1   2    3    4
                                       rms value of the harmonic components
            Total harmonic distortion
                                      rms value of the fundamental component
                                       a   a    a    a
                                                        2 …
                                          2
                                              2
                                                   2
                                          1
                                              2
                                                   3
                                                        4
                                                                        (4.3)
                                               a
                                                 1
              Total harmonic distortion is often abbreviated to thd and is usually
            expressed as a percentage of the fundamental component (either cur-
            rent or voltage).
                                     instantaneous peak value of current
                 Peak or crest factor
                                        rms value of the total current
                                     instantaneous peak value of current
                                                                        (4.4)
                                             a   a    a    a  …
                                                    2
                                                         2
                                                             2
                                               2
                                               1    2    3   4
              For a sinusoidal supply voltage, and where cos   is the power factor
            of the fundamental current component:
                                    Power   v a 1 cos
                                            v a   cos                   (4.5)

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