The Inverter
The Inverter Converts DC to AC. (From Direct current to
Alternating current) An example of Direct current source is the battery. An
example of Alternating current source is the generator or the mains power
supply ie the Public utility Power supply.
AC can be rectified to get DC and DC can be rectified to get AC. The
technique adopted or the components used or the design depends on the intended
use of the final product or the application. Switches and devices that can
operate as a switch are widely used for this purpose. The transistor, mosfet,
(metal oxide seficonductor field effect transistor), oscilators, thyristors and
other circuit elements can be used for this purpose. In Electrical Power Engineering where high
voltages and current are expected, thyristors are used for the design and
construction of the inverter.
The output voltage is periodic. The waveform depends on the
load and most times contains harmonics. At resonance for an RLC
load,(resistive, inductive, capacitive) a sinusoidal waveform is achieved.
Inverters are very useful in DC links for changing the DC
voltage to AC voltage for connection to the existing AC Electrical Power
Network. It is also used for the design and construction of UPS uninterruptable
Power Supply Which is useful where power is not expected to fail. The UPS comes
on when the mains Electrical Power System fails.
As stated earlier on, inverters convert dc Power to AC Power
at some desired output voltage and frequency.
Some Applications are as follows:
Stand-by Power
Supplies
Uninterruptable Power Supplies UPS for companies and other
sensitive systems
Variable speed ac motor drives
Aircraft Power Supplies
Induction heating
Output of DC transmission lines
The output voltage is non – sinusoidal. It therefore
contains some harmonics. These effect the overall performance of the system.
We will take a look at the basic principle of operation of
this inverter.
Output frequency
ω = 2π/T rad/s
Note that the Load Characteristics has to be taken into
consideration. It is possible that the load could have some inductance and
capacitance. If that is the case, the load voltage and current will not reverse
at the same time. The output wave form of the load voltage and current depends
on the load characteristics.
The diode in the circuit will permit load current to flow if
this is the case. This is called the free - wheeling diode.
Disadvantage of the half bridge inverter.
It requires a three wire DC source.
The full – bridge inverter circuit is usually used when a
single – phase ac output is needed.
Power Circuit.
Most Electrical Engineering Power Systems have some
resistances, inductances and capacitances. As a result of this, it is important
to investigate the response of the inverter to an RLC circuit.
Consider an RLC Load (series load) with a voltage source
whose waveform is rectangular and which has an amplitude of V/2 [V] and a
period T. The equivalent circuit is given as shown.
Vs = V/2 [V] : 0<t<T/2 [s]
{#}
Vs = -V/2 [V] : T/2<t<T [s]
After a number of cycles of Vs the time variation
of the of the would have settled down to a periodic form such that,
io = Io1
[A] : t = T/2 [s]
io = - Io1 [A] : t = T/2 s t = 0, T [s]
During the interval, 0<t<T/2 [s],
Vo = V/2 = VR +VL + VC
[V]
Ie
V/2 = Rio + Ldio/dt + (1/C)∫ 0t io
dt +
Vc0 [V] {*}
Where
Vc0 is the voltage across the capacitor (ie the
capacitive part of the load) at t = 0
Differentiating equation {*}
{divide by ‘L’ first}
(d2io/dt2 ) + (R/L) (dio/dt)
+ (1/LC)io = 0 A/s2 {**}
Using initial conditions of eqn {#} a solution of the
equation above {**} gives the load current expression io as a
function of time.
NB: Since the Load voltage Vo is defined, the
current values necessary for rating the inverter components can be obtained
using fourier series.
This means that it is not always necessary to determine an
analytical expression for io.
A qualitative understanding of the time variation of io is
helpful. Some waveforms will be shown below
(i)
Underdamped Oscillatory Load Circuit
(ii)
Overdamped Case With Increased Load-Circuit Resistance
(iii)
Ideal Case for ‘RL’, ‘RC’,’R’ Load Situations
From the curves, it is obvious that the thyristors may start
to conduct at different instants in the half cycle depending on the nature of
the load.
To ensure that the thyristor starts to conduct when
required, each is gated continuously throughout the half-cycle; as shown in the
diagram.
Fourier Series can be used to write an expression for the
output voltage. ‘Vo’
Vo = Σ○○ (2V/nπ)sinnwt [V]
n=1 For n = 1,3,5…………………….
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