Application of L
1-impulse method to the optimization problems in power theory
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:
This inequality causes numerous optimization problems, among which the norm of the current minimization is the most important one:
Whereas the theory of instant-average power values joins both aforementioned methods and uses so-called ‘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 L
1 impulses as an alternative to the Fourier series method. This technique is efficient when the energy is transmitted with highly distorted periodic signals.