3.2 The higher harmonics of a current and a voltage
The higher harmonics in a curve of the rectified voltage
ud
Um
α
α
Figure 3.1
ud = Ud-+ ud ~.
For all circuits of rectifying and inverting at Ld = ∞ and no-load (without taking into account losses)
where ω1 = ωm ,
ω -a line frequency,
ω1 - frequency of 1-th harmonic of a rectified voltage,
m - a multiplicity of pulsations ud,
n - the order of a higher harmonic,
Unm - amplitude of the higher harmonic about n,
n - an initial phase of the higher harmonic about n.
Then
Amplitude cosine component
Amplitude sine component
Period of the first harmonic of the rectified voltage
The rectified voltage we is described by function
For single-phase half-wave, single-phase full-wave with centre tap, a single-phase bridge, three-phase zero circuits
For a three-phase bridge
For the circuit of a double three-phase star with the current-balancing reactor
Then
From here
In per units
With increase fast growth of the higher harmonics would be observed.
3.2.3 The higher harmonics in a curve of a prime current
If Pd there is less than power of supply network, rectifier influence to supply network can be not taken into account, U1 practically is not distorted. If Pd is commensurable with power of the supply network SNW, the higher harmonics of a current will create a voltage drop across supply network reactances witch is proportional to order of the higher harmonic and U1 will be deformed. In this case it is necessary to apply filters.
The order of the higher harmonics of a prime current is
,
where К=1,2,3…
m - a multiplicity of pulsation of Ud.
If γ=0 Ld=∞ and (i.e. the form of i1 is graduated),
where I1(q) - a rms current of q-th harmonic,
I1 (1) - a rms current of 1-st harmonic.
3.3. Power characteristics of the converter
3.3.1. Efficiency
Active losses of a converter are
1) The thyristor losses ∆РT.
2) The transformer losses
∆РTr = ∆РSt+ ∆РCop,
where ∆РSt - steel losses;
∆РCop - Cop-losses in windings.
3) The reactors losses ∆РR (anodic, smoothing and current-balancing).
4) Losses in the auxiliary equipment (a control and regulation system, cooling system) ∆PAux.
∆РSt and ∆РAux are constant and are not load-depending.
For middle-and high-voltage sets
where m - number of thyristors in the circuit,
∆UT - a voltage drop on the thyristor.
More precisely if to take into account current-voltage diagrams of the thyristor
U0
ctg α =
RД
α
UV
iV
where kf - the form factor.
Then, for low-voltage rectifiers
Primary windings of the transformer losses
where n1 - number of primary windings,
R1 - resistance of a primary winding.
Secondary windings losses the transformer
where n2 - number of secondary windings;
R2 - resistance of secondary windings.
Reactor losses
where ∆РSmR – the smoothing reactor losses,
∆РCBR - the current-balancing reactor losses,
∆РAR - the anodic reactor losses.
The core of reactors losses , as a rule, do not take into account.
Thus, at Ld≈∞
At Ld <∞ it is necessary to add a addendum into a denominator
For converters of low power
where ηTh – thyristor block efficiency,
ηTr - transformer efficiency,
ηf – filter efficiency.