BULLETIN of the

POLISH ACADEMY of SCIENCES

TECHNICAL SCIENCES

 BULLETIN of the POLISH ACADEMY of SCIENCES: TECHNICAL SCIENCES
Volume 58, Issue 1, March 2010

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pp 197 - 207

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Application of L1-impulse method to the optimization problems in power theory

M. SIWCZYNSKI and M. JARACZEWSKI
In optimization power theory we can distinguish the three approaches:

  • the theory of instant power values
  • the theory of average power values (integral power)
  • the theory of instant-average power value.

    The theory of instant power uses the instant power and signals values i.e. p (t) = u(t)i(t) whereas the theory of average power uses the energy or average power terms i.e. P = (u(t), i(t)) (the dot the product of signals). The main problem in the average power theory comes from the Schwartz inequality:
    |(u, u)| ≤ ||u|| ||i|| ,

    where ||u|| = √(u, u), ||i|| = √(i, i).
    This inequality causes numerous optimization problems, among which the norm of the current minimization is the most important one:
    ||i|| → min,
    (u, i) - P = 0.

    Whereas the theory of instantaverage power values joins both aforementioned methods and uses socalled 'instant active power':

    The mathematic methods used in these theories derive from the theorems of signals and instant power modulation. This article deals only with the average power theory which uses the L1 impulses as an alternative to the Fourier series method. This technique is efficient when the energy is transmitted with highly distorted periodic signals.
    • Key words:

    periodically timevarying networks, operational calculus, stability, synthesis, optimization

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