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Filters Theory and Applications and Simulation Using PowerFactory Software

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  • #1

    Filters Theory and Applications and Simulation Using PowerFactory Software

    I will try to summarise the theory of filters and applications in power systems.
    Then will show how PowerFactory software can be used in optimal placement in power system network.

    Filters discriminate between input of different frequencies.
    Since electrical signals contain wanted and unwanted components. These components in majority of cases are of different frequencies.
    A filter in ideal situation reject unwanted components and leave wanted components unaffected.
    Tags: 3-phase, engineer, filters, power system, powerfactory
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  • #2
    Thank you admin for featuring my topic

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    • #3
      Click image for larger version Name: Fig01.png Views: 113 Size: 30.3 KB ID: 63

      Filters are designed so that signals are rejected by providing attenuation over band of frequencies. Signals are retained by absence of attenuation (or presence of gain) over other bands for frequencies.

      Filters are classified according to bands of frequencies known as pass bands and stop bands. Four patterns of pass bands and stop bands are to be considered. Sinusoidal steady state response used to categorise filters - ratio of magnitude of input and output sinewaves.
      A = |V2| / |V1|

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      • #4
        (1) Low Pass Filter :

        The pass band is between w = 0 and w = wc
        The stop band is between w = wc and w > wc

        Click image for larger version Name: Fig02.png Views: 126 Size: 85.8 KB ID: 65

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        • #5
          (2) High Pass Filter :

          Complement of low pass filter

          The stop band is between w = 0 and w = wc
          The pass band is between w = wc and w > wc

          Click image for larger version Name: Fig03.png Views: 0 Size: 53.5 KB ID: 67

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          • #6
            (3) Band Pass Filter :

            The pass band is wc1 < w < wc2
            The stop band is between w = 0 ---> w = wc1
            w > wc2


            Click image for larger version Name: Fig04.png Views: 105 Size: 67.0 KB ID: 69

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            • #7
              (4) Band Stop Filter :

              Complement of the band pass filter.

              The pass band is between w = 0 ---> w = wc1
              w > wc2
              The stop band is wc1 < w < wc2

              Notch filter - term used when the stop band is very narrow.



              Click image for larger version Name: Fig05.png Views: 0 Size: 58.0 KB ID: 71

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              • #8
                Design of Low Pass Filter :

                Simple RC circuit can be used to design primitive LP filter.
                Filters are categorised in terms of frequency response which is obtained by substitution s=jw in T(s) = Vo(s) / Vin(s)


                Click image for larger version Name: Fig06.png Views: 107 Size: 30.3 KB ID: 73

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                • #9
                  We need to find transfer function in terms of jw and also phase response.
                  Plotting them as shown below to display characteristics of filter

                  Click image for larger version Name: Fig07.png Views: 0 Size: 39.8 KB ID: 75

                  Click image for larger version Name: Fig08.png Views: 0 Size: 37.6 KB ID: 76


                  The magnitude and phase response in terms of wc
                  Characteristics usually displayed using logarithmic scales.
                  Frequency scale uses log10 (w/wc)
                  angle scale uses decibels or radians.

                  Gain of filter, A = 20 log10 (|T(jw)|) dB
                  By substitution, A = -10 log10 (1 + (w/wc)^2)

                  For low frequencies w/wc << 1 so A --> 0
                  For high frequencies w/wc >> 1 so A --> -20 log10 (w/wc)


                  Click image for larger version Name: Fig09.png Views: 0 Size: 24.7 KB ID: 77
                  Last edited by Rasha; 23 August 2021, 08:00 AM.

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                  • #10
                    Click image for larger version Name: Fig10.png Views: 103 Size: 65.8 KB ID: 79


                    Click image for larger version Name: Fig11.png Views: 101 Size: 253.5 KB ID: 80


                    If know frequencies of wanted signal ws and unwanted interference wi then can choose C and R so that wc lies between ws and wi.
                    • For good suppression of unwanted signal need wc to be as far from wi as possible.
                    • If wc is too close to ws then distortion of signal waveform will result unless ws is a pure sine wave.

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                    • #11
                      Design of Low Pass Filter :

                      Use simple R-C circuit to design LPF, using 0.1 microF and has a cut-off frequency of 3 kHz.
                      Calculate the attenuation at 10 kHz in dB.

                      Click image for larger version Name: Fig12.png Views: 127 Size: 132.3 KB ID: 82

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                      • #12
                        Thank you for topic. That would be useful to share how can power factory handle optimal placement

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                        • #13
                          Great topic.
                          We need application using PowerFactory

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