Modulation for Power Electronic Converters
At present, voltage source converters are mostly used in electrical drives. These converters utilize capacitors in the DC-link to temporarily store electrical energy. Switching the power electronic devices allows the DC voltage to be modulated which can r
- PDF / 4,012,469 Bytes
- 37 Pages / 439.36 x 666.15 pts Page_size
- 105 Downloads / 269 Views
Modulation for Power Electronic Converters
2.1 Introduction At present, voltage source converters are mostly used in electrical drives. These converters utilize capacitors in the DC-link to temporarily store electrical energy. Switching the power electronic devices allows the DC voltage to be modulated which can result in a variable voltage and frequency waveform. The purpose of the modulator is to generate the required switching signals for these switching devices on the basis of user defined inputs. For this purpose, the voltage–time integral was introduced [3], which in turn is tied to the average voltage per sample U (tk ) according to 1 Ts
U (tk ) =
tk +Ts
tk
u (t) dt,
(2.1)
where Ts is a given sample interval and u(t) represents the instantaneous voltage across a single-phase of a load. The introduction of the variable Ts assumes the use of a fixed sampling frequency which is normally judicially chosen higher than the fundamental frequency range required to control electrical machines. The upper sampling frequency limit is constrained by the need to limit the switching losses of the converter semiconductor devices. The ability to control the converter devices in such a manner as to provide the load with a user defined mean reference voltage per sample U ∗ (tk ) is instrumental to control current accurately. This statement can be made plausible by considering the incremental flux linkage for one sample interval of a load in the form of a coil with inductance L and resistance R which may be written as ψ (tk ) =
tk +Ts
tk
(u (t) − Ri (t)) dt.
© Springer Nature Switzerland AG 2020 R. W. De Doncker et al., Advanced Electrical Drives, Power Systems, https://doi.org/10.1007/978-3-030-48977-9_2
(2.2)
17
18
2 Modulation Techniques for Power Electronic Converters
The corresponding incremental change of load current (over a sample interval Ts ) may be written as i (tk ) =
ψ (tk ) L
(2.3)
in the event that magnetic saturation effects may be ignored. This expression can, with the aid of Eq. (2.2), be expressed as i (tk ) =
1 L
tk +Ts tk
u (t) dt −
R L
tk +Ts tk
i (t) dt
(2.4)
which may be reduced to U (tk ) Ts i (tk ) ∼ = L
(2.5)
when the time constant τ = L/R of the load is deemed to be relatively large, i.e., at least by a factor of ten, compared to Ts , as is normally the case for electrical machines. Central to the issue of controlling the incremental current is therefore, according to Eq. (2.5), the ability of the modulator to realize (within the constraint of this unit) the condition U (tk ) = U ∗ (tk )
(2.6)
for each sampling instance. Note that Eq. (2.6) simply states that the switching states of the converter must be controlled by the modulator to ensure that the average voltage (per sample) equals the user defined average reference value to ensure that the actual and reference incremental current change (per sample interval) are equal. How this may be achieved will be outlined in subsequent sections for various converter topologies using an approach taken by Svenss
Data Loading...
