PARK THREEPHASE APPROACH TO ELECTRIC ARC DYNAMIC ANALYSIS

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PARK THREE-PHASE APPROACH TO ELECTRIC ARC DYNAMIC
ANALYSIS

• F. Della Torre S. Leva A.P. Morando
• Dipartimento di Elettrotecnica Politecnico di
  Milano

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Outlines

• The state equations approach is introduced and
  applied to single-phase networks with circuit
  breakers
• After put in evidence the asymmetry of the
  three-phase circuits in presence of circuit
  breakers, the state analysis in terms of phase
  variables is worked out for the three-phase
  network
• The Park transform emphasizes the role of the
  imaginary power on the energetic aspects in the
  three-phase interruption

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Single-Phase Case
Under the systematic aspect the network analysis
adopt as electrical state variables the current
i for the inductors and the voltage v for
capacitors and a state variable rar that
represents the circuit breaker seen as a dynamic
element.
For the topological approach, the inductors are
placed on the chords and the capacitors on the
branches, the breaker can be inserted on the tree
or cotree branches according to the topology of
the network in which is located.
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On the energetic point of view
- the Joule integral of the interruption
phenomenon
Iar,RMS rms arc current Tti-tf time of the
interrupting process
- the electrical breaking work elaborated by the
breaker (as a measure of the thermal stress of
the component)
Par average power elaborated by the arc.
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Three-phase case

• The three distinct arcs may be considered with
  the same constitutive relation rarF(var,iar) but
  the non-linearity of the functional F introduces
  a instantaneous asymmetry.
• The dynamical analysis, not anymore single-phase
  as in the case of symmetric networks, must then
  be referred to the phase variables yabc(t) .
• The three-phase network with arc can be studied
  by the equations state method.
• On the energetic point of view the Park is
  applied the Park quantities are calculated
  starting from the phase quantities.

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- the Park current and voltage vectors
The arc voltage is instantaneously shifted
respect to the Park arc current. It is not
related to any process of energy storage but is
consequence of the non-linearity of the arc.
- the instantaneous Park complex power
imaginary power
real power
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- the Joule/Park integral of the 3ph interruption
phenomenon
- the electrical breaking work elaborated by the
breaker (as a measure of the thermal stress of
the component)
The imaginary power affects, as index of the
three-phase unbalance instantaneously caused by
the arc, the three-phase Joule integral and the
electrical breaking work.
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Conclusions

• The arc phenomena analysis has been included in
  the state equations approach to study the dynamic
  of single-phase and three-phase networks.
• There is no limitation for the arc model and the
  network complexity.
• The three-phase arc causes asymmetry
  consequently the equivalent single-phase approach
  cannot be used.
• Under the energetic point of view, the
  three-phase variables are analyzed by Park
  transformation.
• The sizing power and braking work are greater
  than those calculated by the equivalent
  single-phase model usually adopted.
• Thanks of these energetic results, it is possible
  to design the breaker under study without the use
  of empirical coefficients.