Other useful equations that will be used for the Impedance Method Short Circuit Calculations are:

  1. MVA, Z, V and kV
    MVA={(V/1000)^2}/{Z}

    MVA={{kV}^2}/{Z}

    where:

    V=volts
    kV=kilovolts
    Z=ohms

  2. X, R and Z
    R=Z*cos(atan(X/R))

    X=R*(X/R)

    where:
    X/R = X/R ratio

  3. Transformers
    Z_tp={({%Z}/100)}*{(kV_tp)^2}/{MVA} ohms (referred to primary)

    R_tp={Z_tp}*cos(atan(X/R)) ohms (referred to primary)

    X_tp={R_tp}*(X/R) ohm (referred to primary)

    Z_ts={({%Z}/100)}*{(kV_ts)^2}/{MVA} ohms (referred to secondary)

    R_ts={Z_ts}*cos(atan(X/R)) ohms (referred to secondary)

    X_ts={R_ts}*(X/R) ohm (referred to secondary)

    where:
    kV = Transformer primary or secondary voltage
    X/R = Transformer X/R ratio
    {%Z}= Transformer Impedance

  4. Cables and Reactors
    R_c=r_c*Length/n

    X_c=x_c*Length/n

    Z_c=sqrt{(R_c)^2+{X_c)^2}

    where:
    r_c = Cable per unit resistance
    x_c = Cable per unit reactance
    R_c = Cable total resistance
    X_c = Cable total reactance
    Z_c= Cable total impedance
    n= Number of conductors in parallel per phase
    Length= Cable length

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