Voltage Control

Applets



significance of voltage control

   Typical ranges of quantities

      active power      P =  (-100% ...) 0% ... +100%

      reactive power    Q = -100% ... + 100%

      current           I = 0% ... 100% Ir  (rated or nominal value)

      voltage           U = ?


   why not U = 0 ... 100% in 400 V (low voltage) level ?

      house hold consumers, equipment   95% ... 105%

      => LV  U = 95% ... 105% (acording to country specific standards)


   why not 500 kV in 400 kV voltage level ?

     insulation of lines and cabels, switches

     insulation and saturation of transformers


   why not 300 kV in 400 kV voltage level ?

      consider: PLoad = 3 U I ,  QLoad = 0

      I = PLoad / 3 U

      I high for low U

      reduced transmission capacity
      
      increased losses

         PLoss = R  | I | ^2


      => EHV, HV  U = 90% ... 110%



causes of low voltages


   source voltage

      generator terminal voltage

      transformer ratio / tap setting


  voltage drop

     line length, load current

     S = 3 U * I*

     I = ( P - j Q ) / 3 UL*

     US = UL + ( R + j X ) * I
     
     US = UL + ( R + j X ) * ( P - j Q ) / 3 UL*

     for UL = UL + j 0

     US = UL + ( R P + X Q + j ( X P - R Q ) ) / 3 UL

     real part: aprox. = absolute value = voltage magnitude

     imaginary part (small, phase angle between US and UL)



     for HV and EHV   R << X   (~10%)

     voltage magnitude mainly governed by Q

     phase angle mainly governed by P

     (remember dU/dQ >> dU/dP for transmission lines)



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means of voltage control



generator: limits of power injection

Generator_vsd~Generator1.png Generator_vsd~Generator2.png
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load flow calculations

   Free load flow demo:   Power World Simulator

   given:
   
      P, Q for all load buses

      P, Q or P, U for generator buses / power injections"

      data of lines and transformers


   find:

      U, <)  for all buses

      I, P, Q for all branches

      Q for P,U generators

      active and reactive power losses
         single branch
         total netzwork


   load flow equations => nonlinear set of equations ( 2 x number of buses)

      Newton-Raphson-method


      

Parallel Operation of Power Transformers


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